Пожалуйста, используйте этот идентификатор, чтобы цитировать или ссылаться на этот ресурс:
http://hdl.handle.net/11701/5992
Полная запись метаданных
Поле DC | Значение | Язык |
---|---|---|
dc.contributor.author | Marov, Alexei V. | - |
dc.contributor.author | Uteshev, Alexei Yu. | - |
dc.date.accessioned | 2017-02-09T08:59:08Z | - |
dc.date.available | 2017-02-09T08:59:08Z | - |
dc.date.issued | 2016-12 | - |
dc.identifier.citation | Marov A. V., Uteshev A. Yu. Matrix formalism of the Reed—Solomon codes. Vestnik of Saint Petersburg University. Series 10. Applied mathematics. Computer science. Control processes, 2016, issue 4, pp. 4–17. | en_GB |
dc.identifier.other | 10.21638/11701/spbu10.2016.401 | - |
dc.identifier.uri | http://hdl.handle.net/11701/5992 | - |
dc.description.abstract | The paper is focused onto modification of the involved algorithms of coding and error (i. e., failures and silent data corruptions) correction in the Reed—Solomon codes. These modifications involve matrix formalism and are based on an algorithm for the Vandermonde matrix inversion. For such a matrix V = λi−1 j n i,j=1 the suggested algorithm computes the columns V −1 [1] , . . . ,V −1 [n−1], V −1 [n] of the matrix V −1 recursively, starting from the last column, via the formulas V −1 [n] = Ξ0, V −1 [j] = Ξn−j − σ1V −1 [j+1] − σ2V −1 [j+2] − ·· ·−σn−jV −1 [n] , j = n − 1, n − 2, . . . , 1 . Here Ξk = λk1 /W (λ1), . . . ,λk n/W (λn) , σk = n j=1 λn+k−1 j /W (λj ), k = 1, n, and W(x) = n k=1(x − λk). The obtained result is applied for realization of systematic coding of the n-vector of the information blocks with the aid of multiplication (in an appropriate Galois field) by the matrix K = [ Wi(aN−j−1)], i = 1,m, j = 0, n − 1. Here W (x), = 1,m, denote the basic Lagrange interpolation polynomials generated by the powers of a primitive element of the field, while m stands for the number of redundancy blocks (syndromes). In the framework of this ideology, an error correcting procedure is also realized. The program implementation in C demonstrates high performance results (compared to existing software) with solid perspectives for parallelization. Refs 17. Fig 1. | en_GB |
dc.language.iso | ru | en_GB |
dc.publisher | St Petersburg State University | en_GB |
dc.relation.ispartofseries | Vestnik of Saint Petersburg University. Series 10. Applied Mathematics. Computer Science. Control Processes;Issue 4 | - |
dc.subject | error-correcting codes | en_GB |
dc.subject | Reed—Solomon codes | en_GB |
dc.subject | Vandermonde matrix | en_GB |
dc.title | Matrix formalism of the Reed—Solomon codes | en_GB |
dc.type | Article | en_GB |
Располагается в коллекциях: | Issue 4 |
Файлы этого ресурса:
Файл | Описание | Размер | Формат | |
---|---|---|---|---|
01-Marov.pdf | 368 kB | Adobe PDF | Просмотреть/Открыть |
Все ресурсы в архиве электронных ресурсов защищены авторским правом, все права сохранены.