An algebraic and geometric approach of linear cyclic, BCH codes
Metrics that agree on the support of vectors and nearest neighbor decoding
Algebraic and Geometric Fundamentals of Codes: Linear, Cyclic and BCH.
| Full text | |
| Author(s): |
Total Authors: 3
|
| Affiliation: | [1] Quaid I Azam Univ, Dept Math, Islamabad 45320 - Pakistan
[2] Univ Estadual Paulista, IBILCE, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | Anais da Academia Brasileira de Ciências; v. 85, n. 3, p. 863-872, 2013-09-00. |
| Abstract | |
For a given binary BCH code Cn of length n = 2s - 1 generated by a polynomial of degree r there is no binary BCH code of length (n + 1)n generated by a generalized polynomial of degree 2r. However, it does exist a binary cyclic code C(n+1)n of length (n + 1)n such that the binary BCH code Cn 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 Cn. Furthermore, an algorithm proposed facilitates in a decoding of a binary BCH code Cn through the decoding of a binary cyclic code C(n+1)n, while the codes Cn 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 |