# Device for finding and correcting errors in codes of polynomial system of residue classes based on zeroing

FIELD: computer engineering, in particular, modular neuro-computer means, possible use for finding and correcting errors in modular codes of polynomial residual class system.

SUBSTANCE: in accordance to invention, polynomial residual class system is used, in which as system base minimal polynomials p_{i}(z), i=1,2,...,7, are used, determined in extended Galois fields GF(2^{5}) and neuron network technologies, and also modified zeroing constants determined in current polynomial residual class system are used in parallel.

EFFECT: increased speed of detection and correction of errors in modular codes of polynomial residual class system.

2 dwg, 7 tbl

The invention relates to computing, and in particular to modular neurocomputer means, and is intended to perform a search and error correction modular polynomial codes system classes deductions (PSCW).

The aim of the invention is to increase, speed, location and depth errors in modular code PSCW for correction result based on the method of Oleviste. The goal is achieved at the expense of transition from sequential nature of the operation of Oleviste to parallel subtraction constants Oleviste, as well as the use of neural network basis and performing operations on polynomial system classes deductions extended Galois fields GF(2^{ν}).

The technical result achieved in the implementation of the claimed invention is to increase the speed of detection and correction of errors in modular codes PSCW.

This technical result is achieved due to the use of polynomial systems classes deductions (PSCW), in which the base system uses minimal polynomials p_{i}(z), i=1, 2, ..., k+r, defined in the extended Galois fields GF(2^{ν}), and neural network technology, as well as the parallel application of modified constants Oleviste defined in this PSCW.

If the foundations of the deposits of the new algebraic system to choose the minimal polynomial p_{
i}(z) GF(p^{ν}), then any polynomial A(z), satisfying the condition

A(z)∈P_{floor},

where

can be represented as n-dimensional vectors

where, i=1, 2, ..., k+r.

As a comparison to the same module can pocino to add, subtract and multiply, sum, difference and product of two polynomials A(z) and B(z), respectively having modular code (α_{1}(z),α_{2}(z),...,α_{k+r}(z)) and (β_{1}(z),β_{2}(z),...,β_{k+r}(z)) the following relations are true:

Thus, performing operations on operands in the extended Galois field GF(R^{ν}) are performed independently for each of the modules p_{i}(z)that indicates the concurrency of this algebraic system.

In addition, the feature PSCW consists in the fact that the independence of the information processing on the grounds PSCW allows not only to improve the speed and accuracy of processing, but also to ensure the detection and correction of errors during the operation of the computing device class deductions. If the range of possible changes in the encoded set of polynomial constraints, the EU is ü to choose k out of n bases PSCV (k<
n), this will allow splitting the full range of P_{full}(z) extended Galois fields GF(p^{ν}) into two disjoint subsets.

The first subset is called the working range and is determined by the expression

The polynomial A(z) with coefficients from GF(p) will be considered resolved if and only if it is a zero interval of the full range of P_{full}(z), that is, by the working range of A(z)∈P_{slave}(z).

The second subset of GF(R^{ν}determined by the product of r=n-k control grounds

specifies the set of forbidden combinations. If A(z) is an element of the second subset, it is believed that this combination contains an error. Thus, the location of the polynomial A(z) relative to the two data subsets allow us to determine whether the code combination A(z)=(α_{1}(z),α_{2}(z),...,α_{k+r}(z)) is allowed, or contains invalid characters.

To locate A(z)=(α_{1}(z), α_{2}(z),..., α_{k+r}(z)) (Akutski IA, yuditsky DI Machine arithmetic in residual classes. - M.: Soviet radio, 1968. - 439 S. (str-194)) proposed to use the method of Oleviste, in which lane the course of the original polynomial to a polynomial of the form

using serial conversions where no none outside the operating range of the system.

According to this method, Oleviste is sequential subtraction from the original polynomial presented in modular code, some minimal polynomial constants of Oleviste such that the polynomial A(z) is sequentially converted to a polynomial of the form

where- constant Oleviste on the first basis of p_{1}(z).

Then, from the obtained result is subtracted following constant Oleviste to obtain polynomial

whereon the second basis p_{2}(z), and so on. Continuing this process for k iterations, the result

The application of the method of Oleviste allows us to consistently obtain the smallest polynomial multiple of first p_{1}(z), then the polynomial is a multiple of p_{1}(z)p_{2}(z), and in the end - times operating range.

If the serial execution procedures Oleviste will receive a zero result, ie,

x_{k+1}(z)=0, x_{k+2}(z)=0,...,x_{k+r}(z)=0,

it shows that the similar combination of A(z), presented in a modular code does not contain errors. Otherwise, modular code A(z) - contains errors.

The main disadvantage of the known method Oleviste is the sequential nature of the computational process. This is due primarily to the fact that constants Oleviste represent the smallest possible numbers of the form

where

To improve the performance of the procedures of Oleviste possible by modifying the constants of Oleviste M_{i}(z). Leaving unchanged the condition of absenteeism constants Oleviste M_{i}(z) outside the operating rangewill take the last value of the product of residues of work bases on the value of orthogonal bases nonredundant system grounds

where- orthogonal basis, nonredundant system reason; i=1, 2, ..., k.

Then if we put the condition that A(z)∈P_{slave}(z), wherethen the polynomial A(z)=(α_{1}(z),α_{2}(z)...,α_{k}(z)) according to Chinese theorem rests (WHO) can be represented in the form

Each term of the expression (9) p is ecstasy a

We substitute the expression (8) into the equality (10). Get the

Therefore, the values of the residues on the test grounds will be determined

Hence, the difference of the polynomial A(z) and modified constants Oleviste M_{i}(z), i=1, 2, ..., k, pseudoorthogonal forms obtained according to (4.5), sets the value of the normalized trace of a polynomial

Proceeding from the condition that the modified constants Oleviste M_{i}(z) are orthogonal bases nonredundant system grounds PSCW, the operation of Oleviste (13) can be implemented in parallel.

To reduce the volume of stored values of the constants Oleviste M_{i}(z), i=1, 2, ..., k, represent the residue number α_{i}(z) in the form

wherethe elements of the field GF(2); j=0, 1, ..., ordp_{i}(z)-1.

Then true

Thus, instead of storingconstants Oleviste M_{i}(z) it is enough to determine ordp_{i}(z) constants.

Consider PSCW defined in the field GF(2^{5}). In table 1 present values of operating and control bases PSCW and dynamic range for the extended is Olya Galois.

Table 1 | ||

The base and the dynamic range of the field GF(2^{5}) | ||

Base PSCW | Operating range | |

Working | Control | PSCW |

p_{1}(z)=z+1 | p_{6}(z)=z^{5}+z^{2}+1 | z^{21}+z^{19}+z^{16}+z^{13}+ |

p_{2}(z)=z^{5}+z^{3}+1 | p_{7}(z)=z^{5}+z^{3}+z^{2}+z+1 | +z^{11}+z^{9}+z^{8}+z^{6}+ |

p_{3}(z)=z^{5}+z^{4}+z^{2}+z+1 | +z^{3}+z^{2}+z+1 | |

p_{4}(z)=z^{5}+z^{4}+z^{3}+z+1 | ||

p_{5}=z^{5}+z^{4}+z^{3}+z^{2}+1 |

Orthogonal bases nonredundant system grounds PSCW p_{1}(z), p_{2}(z), R_{3}(z), p_{4}(z), p_{5}(z) take the following values

B_{1} ^{*}(z)=z^{20}+z^{19}+z^{15}+z^{14}+z^{13}+z^{10}+z^{9}+z^{7}+z^{6}+z^{2}+1;

B_{2} ^{*}(z)=z^{16}+z^{8}+z^{4}+z^{2}+z+1;

B_{3} ^{*}(z)=z^{20}+z^{18}+z^{16}+z^{15}+z^{13}+z^{12}+z^{11}+z^{10}+z^{6}+z^{3}+z;

B_{4} ^{*}(z)=z^{19}+z^{18}+z^{16}+z^{15}+z^{14}+z^{13}+z^{8}+z^{7}+z^{6}+z^{5}+z^{4}+z;

B_{l} ^{*}(z)=z^{16}+z^{15}+z^{14}+z^{13}+z^{12}+z^{11}+z^{9}+z^{6}+z^{5}+z^{3}+z+1.

Determine all values of works of degrees z^{j}on orthogonal bases B_{i} ^{*}(z), given the impossibility of going beyond the working range of the P_{slave}(z)=z^{21}+z^{19}+z^{16}+z^{13}+z^{11}+z^{9}+z^{8}+z^{6}+z^{3}+z^{2}+z+1. The obtained values of the modified constants Oleviste presented in table 2.

Table 2 | |||||||

Constants Oleviste for the field GF(2^{5}) | |||||||

α_{1}(z) | α_{2}(z) | α_{3}(z) | α_{4}(z) | α_{5}(z) | α_{6}(z) | α_{7}(z) | |

z^{0}B_{1} ^{*}(z) | 1 | 0 | 0 | 0 | 0 | z^{2} | z |

z^{0}B_{2} ^{*}(z) | 0 | 1 | 0 | 0 | 0 | 1 | 1 |

z^{1}B_{2} ^{*}(z) | 0 | z | 0 | 0 | 0 | z | z |

z^{2}B_{2} ^{*}(z) | 0 | z^{2} | 0 | 0 | 0 | z^{2} | z^{2} |

z^{3}B_{2} ^{*}(z) | 0 | z^{3} | 0 | 0 | 0 | z^{3} | z^{3} |

z^{4}B_{2} ^{*}(z) | 0 | z^{4} | 0 | 0 | 0 | z^{4} | z^{4} |

z^{0}B_{3} ^{*}(z) | 0 | 0 | 1 | 0 | 0 | z^{4}+z | z^{4}+1 |

z^{1}B_{3} ^{*}(z} | 0 | 0 | z | 0 | 0 | z^{3}+z^{2}+1 | z^{3}+z+1 |

z^{2}B_{3} ^{*}(z) | 0 | 0 | z^{2} | 0 | 0 | z^{4}+z^{3}+z | z^{4}+z^{2}+z |

z^{3}B_{3} ^{*}(z) | 0 | 0 | z^{3}
| 0 | 0 | z^{4}+1 | z+1 |

z^{4}B_{3} ^{*}(z) | 0 | 0 | z^{4} | 0 | 0 | z^{2}+z+1 | z^{2}+z |

z^{0}B_{4} ^{*}(z) | 0 | 0 | 0 | 1 | 0 | z^{2} | z+1 |

z^{1}B_{4} ^{*}(z) | 0 | 0 | 0 | z | 0 | z^{3} | z^{2}+z |

z^{2}B_{4} ^{*}(z) | 0 | 0 | 0 | z^{2} | 0 | z^{4}+z^{3}+z^{2} | z^{3}+z |

z^{3}B_{4} ^{*}(z) | 0 | 0 | 0 | z^{3} | 0 | z^{4}+z | z^{4}+z^{2} |

z^{4}B_{4} ^{*}(z) | 0 | 0 | 0 | z^{4} | 0 | z^{3}+z+1 | z^{3}+z^{2}+1 |

z^{0}B_{5} ^{*}(z) | 0 | 0 | 0 | 0 | 1 | z^{4}+z | z^{4} |

z^{1}B_{5} ^{*}(z) | 0 | 0 | 0 | 0 | z | 1 | z^{3}+z^{2}+z+1 |

z^{2}B_{5} ^{*}(z) | 0 | 0 | 0 | 0 | z^{2} | z | z^{4}+z^{3}+z^{2}+z |

z^{3}B_{5} ^{*}(z) | 0 | 0 | 0 | 0 | z^{3} | z^{2} | z^{4}+z+1 |

z^{4}B_{5} ^{*}(z) | 0 | 0 | 0 | 0 | z^{4} | z^{3} | z^{3}+1 |

If ordered in excess PSCW extended Galois fields GF(p^{ν}for which fair ord_{p1}(z)≤ordp_{2}(z)≤...≤ordp_{k}(z) for two test bases p_{k+1}(z) and p_{k+2}(z) the following relation holds :

they determine the location and magnitude of the error on any basis.

Let us consider an example. Let the field GF(2^{5}), which sets forth the operating and control Foundation according to table 1, set - polynomial A(z)=z^{6}+z^{5}+z^{4}+1, This polynomial belongs to P_{slave}(z). Think of a modular code

A(z)=z^{6}+z^{5}+z^{4}+1=(0,z^{3}+z,z^{4}+z^{3}+z^{2}+z+1,z^{2}+z+1,z^{4}+z^{3}+z^{2}+z,0).

Will carry out consistently the procedure of Oleviste. At the first stage by subtracting modulo 2 received

The value of M_{2}(z) is obtained according to expression (15) by summing the values

M_{2}(z)=z^{3}B_{2} ^{*}(z)+zB_{2} ^{*}(z)=(0, z^{3}, 0, 0, 0, z^{3}, z^{3})+(0, z, 0, 0, 0, z, z)=(0, z^{3}+z, 0, 0, 0, z^{3}+z, z^{3}+z).

At the second stage of Oleviste have

In the third stage of Oleviste received

In the fourth stage of Oleviste have

Thus, the polynomial A(z) does not contain errors.

Table 3 | |||

The dependence of the location and depth errors from the results of the procedure of Oleviste | |||

The result of Oleviste | Error in modular code | ||

x_{6}(z) | x_{7}(z) | depth | base |

z^{2} | z | 1 | p_{1}(z)=z+1 |

1 | 1 | 1 | p_{2}(z)=z^{5}+z^{3}+1 |

z | z | z | |

z^{2} | z^{2} | z^{2} | |

z^{3} | z^{3} | z^{3} | |

z^{4} | z^{4} | z^{4} | |

z^{4}+z | z^{4}+1 | 1 | p_{3}(z)=z^{5}+z^{4}+z^{2}+z+1 |

z^{3}+z^{2}+1 | z^{3}+z+1 | z | |

z^{4}+z^{3}+z | z^{4}+z^{2}+z | z^{2} | |

z^{4}+1 | z+1 | z^{3} | |

z^{2}+z+1 | z^{2}+z | z^{4} | |

z^{2} | z+1 | 1 | p_{4}(z)=z^{5}+z^{4}+z^{3}+z+1 |

z^{3} | z^{2}+z | z | |

z^{4}+z^{3}+z^{2} | z^{3}+z | z^{2} | |

z^{4}+1 | z^{4}+z^{2} | z^{3} | |

z^{3}+z+1 | z^{3}+z^{2}+1 | z^{4} | |

z^{4}+z | z^{4} | 1 | p_{5}(z)=z^{5}+z^{4}+z^{3}+z^{2}+1 |

1 |
z^{3}+z^{2}+z+1 | z | |

z | z^{4}+z^{3}+z^{2}+z | z^{2} | |

z^{2} | z^{4}+z+1 | z^{3} | |

z^{3} | z^{3}+1 | z^{4} | |

1 | 0 | 1 | p_{6}(z)=z^{5}+z^{3}+1 |

z | 0 | z | |

z^{2} | 0 | z^{2} | |

z^{3} | 0 | z^{3} | |

z^{4} | 0 | z^{4} | |

0 | 1 | 1 | p_{7}(z)=z^{5}+z^{3}+z^{2}+z+1 |

0 | z | z | |

0 | z^{2} | z^{2} | |

0 | z^{3} | z^{3} | |

0 | z^{4} | z^{4} |

Suppose the error occurred on the first substrate. Then have

A*(z)=(1, z^{3}+z, z^{4}+z^{3}+z^{2}+z+1, z^{2}+z+1, z^{3}+z+1,z^{4}+z^{3}+z^{2}+z, 0).

Will carry out consistently the procedure of Oleviste. At the first stage by subtracting modulo 2 received

The second stage is Oleviste have

In the third stage of Oleviste received

In the fourth stage of Oleviste have

In the fourth stage of Oleviste have

As a result of Oleviste was obtained a non-zero result, which indicates the presence of errors in modular code.

Depending on the magnitude of the syndrome of the error correction is

where (0,...,Δα_{i}(z),...,0) - vector of errors modular code; Δα_{i}(z) - depth error for the i-th module;.

According to table 3, which shows the dependence of the location and depth errors from the results of the procedure of Oleviste, for the measured x_{6}(z)=z^{2}x_{7}(z)=z have that the error occurred on the first substrate and the depth is equal to 1. Then the original polynomial has the form

A*(z)+(1, 0, 0, 0, 0, 0, 0)=(0, z^{3}+z, z^{4}+z^{3}+z^{2}+z+1, z^{2}+z+1, z^{3}+z+1, z^{4}+z^{3}+z^{2}+z, 0).

The structure of the device detection and error correction codes, polynomial system classes deductions on the basis of Oleviste presented in figure 1.

It includes: an input unit 1, block Oleviste 2, memory block 3, the adders 4, 5, 6, 7, 8,9, 10, the output device 11.

The operation of the device is as follows.

On input 1 device detection and error correction codes, polynomial system classes deductions on the basis of Oleviste served controlled number represented in polynomial form

A(z)=(α_{1}(z), α_{2}(z), α_{3}(z), α_{4}(z), α_{5}(z), α_{6}(z), α_{7}(z)).

where α_{i}(z) is the remainder polynomial A(z) modulo p_{i}(z); p_{1}(z), R_{2}(z), p_{3}(z), p_{4}(z), p_{5}(z) - working base system PSCW GF(2^{5}); p_{6}(z), p_{7}(z) - control reasons. The input device is connected to the inputs of the block Oleviste 2. From the output of the block Oleviste calculated values of x_{6}(z), x_{7}(z) are fed to the inputs of the memory block 3 and pick out the appropriate constant error (0,...,Δα_{i}(z),...,0), i=1, 2, 3, 4, 5, 6, 7. This constant error is fed to the second inputs of corrective adders 4, 5, 6, 7, 8, 9, 10 accordingly, on the grounds p_{1}(z), R_{2}(z), R_{3}(z), p_{4}(z), p_{5}(z), p_{6}(z), p_{7}(z), where it is summed with the received first input values α_{1}(z), α_{2}(z), α_{3}(z), α_{4}(z), α_{5}(z), α_{6}(z), α_{7}(z)supplied from the input device 1. Fixed value of A(z) according to the equality (17) with exit to rectitude adders 4-10 applied to the output 11 of the device.

Block Oleviste presented in figure 2.

It consists of: the first layer of neurons 12-42, the second layer of neurons 43-52.

Block Oleviste is a two-layer neural network. The first layer contains 31 neuron. Input neurons 12 in binary code arrives balance α_{1}(z) on the basis of p_{1}(z)=z+1. Input neurons 13-17 arrives balance α_{2}(z) on the basis of p_{2}(z)=z^{5}+z^{3}+1, and the high order bit is served by 13 the neuron, and the youngest is 17 the neuron. Input neurons 18-22 arrives balance α_{3}(z) on the basis of p_{3}(z)=z^{5}+z^{4}+z^{2}+z+1, and the high-order is served on 18 neuron, and the youngest is 22 neuron. Input neurons 23-27 arrives balance α_{4}(z) on the basis of p_{4}(z)=z^{5}+z^{4}+z^{3}+z+1, and the high order bit is served by 23 the neuron, and the youngest is 27 the neuron. Input neurons 28-32 arrives balance α_{5}(z) on the basis of p_{5}(z)=z^{5}+z^{4}+z^{3}+z^{2}+1, and the high-order is served on 28 neuron, and the youngest is 32 neuron. On neurons 33-37 supplied binary code α_{6}(z) by the first control module p_{6}(z)=z^{5}+z^{2}+1, and the high order bit is served by 33 neuron, and the younger at 37 neuron. On neurons 38-42 in binary code is supplied in binary code α_{7}(z) on the second control module p_{7}(z)=z^{5}+z^{3}+z^{2}+z+1, moreover, the high order is served on the neuron 38,
and the youngest at 42 neuron. The second layer of the neural network contains 10 neurons that perform the basic operation of summing modulo two, according to the expression (13), and the first five neurons 43-47 determine the value of x_{6}(z), the remaining neurons 48-52 determine the value of x_{7}(z). The inputs of the neuron 43 of the second layer are connected to the outputs of neurons 13, 19, 20, 22, 24, 25, 32, 33 neurons of the first layer. The inputs of the neuron 44 of the second layer are connected to the outputs of neurons 14, 20, 21, 23, 25, 26, 28, 34 neurons of the first layer. The inputs of the neuron 45 of the second layer are connected to the outputs of neurons 12, 15, 18, 21, 25, 27, 29, 35 neurons of the first layer. The inputs of the neuron 46 of the second layer are connected to the outputs of neurons 16, 18, 20, 22, 23, 30, 32, 36 neurons of the first layer. The inputs of the neuron 47 of the second layer are connected to the outputs of neurons 17, 18, 19, 21, 23, 24, 31, 37 neurons of the first layer. The inputs of the neuron 48 of the second layer are connected to the outputs of neurons 13, 20, 22, 24, 29, 30, 31, 38 neurons of the first layer. The inputs of the neuron 49 of the second layer are connected to the outputs of neurons 14, 21, 23, 25, 28, 30, 31, 39 neurons of the first layer. The inputs of the neuron 50 of the second layer is connected to the outputs of neurons 15, 18, 20, 23, 26, 30, 31, 40 neurons of the first layer. The inputs of the neuron 51 of the second layer is connected to the outputs of neurons 12, 16, 18, 19, 20, 21, 24, 25, 26, 27, 29, 30, 31, 41 neurons of the first layer. The inputs of the neuron 52 of the second layer is connected to the outputs of neurons 17, 19, 21, 22, 23, 27, 28, 29, 31, 42 neurons of the first layer. High values of the results of the zero is Itachi control on the grounds x_{
6}(z) and x_{7}(z), respectively, are calculated in neurons 43 and 48.

Consider the process unit Oleviste examples. Let the input device detection and error correction codes, polynomial system classes deductions on the basis of Oleviste was filed modular code A(z)=(0, z^{3}+z, z^{4}+z^{3}+z^{2}+z+1, z^{2}+z-1, z^{4}+z^{3}+z^{2}+1, 0). This code is fed to the inputs of the neurons of the first layer of block Oleviste. The signals at the output of the neurons of the first layer shown in table 4.

The signals from the outputs of the neurons of the first layer are received at the respective inputs of the neurons of the second layer. Table 5 presents the values of the signals at the input and output neurons of the second layer. The symbol "-" indicates there is no connection between neurons of the second and the first layer. Obtained a null result suggests that this combination does not contain errors.

Assume that the error occurred on the first substrate. Then the modular combination is

A*(z)=(1, z^{3}+z, z^{4}+z^{3}+z^{2}+z+1, z^{2}+z+1, z^{3}+z+1, z^{4}+z^{3}+z^{2}+z, 0)

This code is fed to the inputs of the neurons of the first layer of block Oleviste. The signals at the output of the neurons of the first layer are presented in table 6.

The signals from the outputs of the neurons of the first layer are received at the respective inputs of the neurons of the second layer. the table 7 presents the values of the signals at the input and output neurons of the second layer.

In the procedure, parallel Oleviste, was the result different from zero, i.e. x_{6}(z)=z^{2}x_{7}(z)=z. Therefore, the modular combination, an input device, contains an error.

According to table 3, which shows the dependence of the location and depth errors from the results of the procedure of Oleviste, for the measured x_{6}(z)=z^{2}x_{7}(z)=z have that the error occurred on the first substrate and the depth is equal to 1.

Table 4 | |

The signals at the output of the neurons of the first layer | |

Neuron | The signal |

12 | 0 |

13 | 0 |

14 | 1 |

15 | 0 |

16 | 1 |

17 | 0 |

18 | 1 |

19 | 1 |

20 | 1 |

21 | 1 |

22 | 1 |

23 | 0 |

24 | 0 |

25 | 1 |

26 | 1 |

27 | 1 |

28 | 0 |

29 | 1 |

30 | 0 |

31 | 1 |

32 | 1 |

33 | 1 |

34 | 1 |

35 | 1 |

36 | 1 |

37 | 0 |

38 | 0 |

39 | 0 |

40 | 0 |

41 | 0 |

42 | 0 |

Table 5 | ||||||||||

The signals at the output of the neurons of the second layer | ||||||||||

52 | 51 | 50 | 49 | 48 | 47 | 46 | 45 | 44 | 43 | |

- | 0 | - | - | - | - | - | 0 | - | - | 12 |

- | - | - | - | 0 | - | - | - | - | 0 | 13 |

- | - | - | 1 | - | - | - | 1 | - | 14 | |

- | - | 0 | - | - | - | - | 0 | - | - | 15 |

- | 1 | - | - | - | - | 1 | - | - | - | 16 |

0 | - | - | - | - | 0 | - | - | - | - | 17 |

- | 1 | 1 | - | - | 1 | 1 | 1 | - | 18 | |

1 | 1 | - | - | - | 1 | - | - | - | 1 | 19 |

- | 1 | 1 | - | 1 | - | 1 | - | 1 | 1 | 20 |

1 | 1 | - | 1 | - | 1 | - | 1 | 1 | - | 21 |

1 | - | - | - | 1 | - | 1 | - | - | 1 | 22 |

0 | - | 0 | 0 | - | 0 | 0 | - | 0 | - | 23 |

- | 0 | - | - | 0 | 0 | - | - | - | 0 | 24 |

- | 1 | - | 1 | - | - | - | 1 | 1 | 1 | 25 |

- | 1 | 1 | - | - | - | - | - | 1 | - | 26 |

1 | 1 | - | - | - | - | - | 1 | - | - | 27 |

0 | - | - | 0 | - | - | - | - | 0 | - | 28 |

1 | 1 | - | - | 1 | - | - | 1 | - | - | 29 |

- | 0 | 0 | 0 | 0 | - | 0 | - | - | - | 30 |

1 | 1 | 1 | 1 | 1 | 1 | - | - | - | - | 31 |

- | - | - | - | - | - | 1 | - | - | 1 | 32 |

- | - | - | - | - | - | - | - | - | 1 | 33 |

- | - | - | - | - | - | - | - | 1 | - | 34 |

- | - | - | - | - | - | - | 1 | - | - | 35 |

- | - | - | - | - | - | 1 | - | - | - | 36 |

- | - | - | - | - | 0 | - | - | - | - | 37 |

- | - | - | 0 | - | - | - | - | -- | 38 | |

- | - | - | 0 | - | - | - | - | - | - | 39 |

- | - | 0 | - | - | - | - | - | - | - | 40 |

- | 0 | - | - | - | - | - | - | - | - | 41 |

0 | - | - | - | - | - | - | - | - | - | 42 |

0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | Output |

Table 6 | |

The signals at the output of the neurons of the first layer (error) | |

Neuron | The signal |

12 | 1 |

13 | 0 |

14 | 1 |

15 | 0 |

16 | 1 |

17 | 0 |

18 | 1 |

19 | 1 |

20 | 1 |

21 | 1 |

22 | 1 |

23 | 0 |

24 | 0 |

25 | 1 |

26 | 1 |

27 | 1 |

28 | 0 |

29 | 1 |

30 | 0 |

31 | 1 |

32 | 1 |

33 | 1 |

34 | 1 |

35 | 1 |

36 | 1 |

37 | 0 |

38 | 0 |

39 | 0 |

40 | 0 |

41 | 0 |

42 | 0 |

Table 7 | ||||||||||

The signals at the output of the neurons of the second layer (error) | ||||||||||

52 | 51 | 50 | 49 | 48 | 47 | 46 | 45 | 44 | 43 | |

- | 1 | - | - | - | - | - | 1 | - | - | 12 |

- | - | - | - | 0 | - | - | - | 0 | 13 | |

- | - | - | 1 | - | - | - | - | 1 | - | 14 |

- | - | 0 | - | - | - | - | 0 | - | - | 15 |

- | 1 | - | - | - | - | 1 | - | - | - | 16 |

0 | - | - | - | - | 0 | - | - | - | 17 | |

- | 1 | 1 | - | - | 1 | 1 | 1 | - | - | 18 |

1 | 1 | - | - | - | 1 | - | - | - | 1 | 19 |

- | 1 | 1 | - | 1 | - | 1 | - | 1 | 1 | 20 |

1 | 1 | - | 1 | - | 1 | - | 1 | 1 | - | 21 |

1 | - | - | 1 | - | - | 1 | - | - | 1 | 22 |

0 | - | 0 | 0 | - | 0 | 0 | - | 0 | - | 23 |

- | 0 | - | - | 0 | 0 | - | - | - | 0 | 24 |

- | 1 | - | 1 | - | - | - | 1 | 1 | 1 | 25 |

- | 1 | 1 | - | - | - | - | - | 1 | - | 26 |

1 | - | - | - | - | - | 1 | - | - | 27 | |

0 | - | - | 0 | - | - | - | - | 0 | - | 28 |

1 | 1 | - | - | 1 | - | - | 1 | - | - | 29 |

- | 0 | 0 | 0 | 0 | - | 0 | - | - | - | 30 |

1 | 1 | 1 | 1 | 1 | 1 | - | - | - | - | 31 |

- | - | - | - | - | - | 1 | - | - | 1 | 32 |

- | - | - | - | - | - | - | - | - | 1 | 33 |

- | - | - | - | - | - | - | - | 1 | - | 34 |

- | - | - | - | - | - | - | 1 | - | - | 35 |

- | - | - | - | - | - | 1 | - | - | - | 36 |

- | - | - | - | - | 0 | - | - | - | 37 | |

- | - | - | - | 0 | - | - | - | - | - | 38 |

- | - | - | 0 | - | - | - | - | - | - | 39 |

- | - | 0 | - | - | - | - | - | - | - | 40 |

- | 0 | - | - | - | - | - | - | - | - | 41 |

0 | - | - | - | - | - | - | - | - | - | 42 |

0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | Output |

Device detection and error correction on the basis of Oleviste codes polynomial system classes deductions (PSCW) in the original polynomial A(z)=(α_{1}(z),...,α_{i}(z)), where α_{i}(Z) is the remainder polynomial A(z) modulo p_{i}(z), i=(1,..., 7), a p_{1}(z), R_{2}(z), R_{3}(z), p_{4}(z), p_{5}(z) - working base system PSCW GF(2^{5}), R_{6}(z), p_{7}(z) - control of the base, characterized in that the device contains an input, which is connected to the inputs of the block Oleviste representing a two-layer neural network, the first layer which contains 31 neuron, and the second layer of ten neurons that perform the basic operation of summing module, the inputs of the first neuron of the second layer are connected to the outputs 2, 8, 9, 11, 13, 14, 21, 22 neurons of the first layer, the inputs of the second neuron of the second layer are connected to the outputs 2, 9, 10, 12, 14, 15, 17, 23 neurons the first layer, the inputs of the third neuron of the second layer are connected to the outputs 1, 4, 7, 10, 14, 16, 18, 24 neurons of the first layer, the fourth inputs of the neuron of the second layer are connected to the outputs 5, 7, 9, 11, 12, 19, 21, 25 neurons of the first layer, the input is atogo neuron of the second layer are connected to the outputs 6,
7, 8, 10, 12, 13, 20, 26 neurons of the first layer, the inputs of the sixth neuron of the second layer are connected to the outputs 2, 9, 11, 13, 18, 19, 20, 27 neurons of the first layer, the inputs of the seventh neuron of the second layer are connected to the outputs 3, 10, 12, 14, 17, 19, 20, 28 neurons of the first layer, the inputs of the eighth neuron of the second layer are connected to the outputs 4, 7, 9, 12, 15, 19, 20, 29 neurons of the first layer, the inputs of the ninth neuron of the second layer is connected to the outputs 1, 5, 7, 8, 9, 10, 13, 14, 15, 16, 18, 19, 20, 30 neurons of the first layer, the inputs of the tenth neuron of the second layer is connected to the outputs 6, 8, 10, 11, 12, 16, 17, 18, 20, 31 neurons of the first layer, the input unit Oleviste serves the values of the residues α_{i}(z), respectively, the outputs of block Oleviste connected respectively to the inputs of the memory block containing the error constants whose outputs are connected to the second inputs of the seven corrective adders, respectively, the first inputs mentioned adders are connected to the input device, and correcting the adders perform the summation arriving at their first inputs values α_{i}(z) with corresponding constants of the error on the grounds p_{i}(z), arriving at the second input of the above adders, respectively, the outputs of corrective adders are output devices.

**Same patents:**

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1 dwg, 1 app

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