Groups and noncommutative algebra: interactions and applications
Introduction to finite fields and to algebraic error-correcting codes
Superregular matrices, product codes and cryptographic sequences
Full text | |
Author(s): |
Shah, Tariq
;
Khan, Mubashar
;
De Andrade, Antonio A.
Total Authors: 3
|
Document type: | Journal article |
Source: | Anais da Academia Brasileira de Ciências; v. 85, n. 3, p. 10-pg., 2013-09-01. |
Abstract | |
For a given binary BCH code C-n of length n = 2(s) - 1 generated by a polynomial g(x) is an element of F-2[x] of degree r there is no binary BCH code of length (n + 1)n generated by a generalized polynomial g(x(1/2)) is an element of F-2[x 1/2 Z >= 0] of degree 2r. However, it does exist a binary cyclic code C(n+l)n of length (n + 1)n such that the binary BCH code C-n is embedded in C(n+1)n. Accordingly a high code rate is attained through a binary cyclic code C(n+1)n for a binary BCH code C-n. Furthermore, an algorithm proposed facilitates in a decoding of a binary BCH code C-n through the decoding of a binary cyclic code C(n+1)n, while the codes C-n and C(n+1)n have the same minimum hamming distance. (AU) | |
FAPESP's process: | 11/03441-2 - Codes and lattices with applications |
Grantee: | Antonio Aparecido de Andrade |
Support Opportunities: | Research Grants - Visiting Researcher Grant - International |