Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902925 | Discrete Mathematics | 2018 | 33 Pages |
Abstract
In this paper, we consider cyclic codes of odd length n over the local, non-chain ring R=Z2s[u]âãukã = Z2s+uZ2s+â¦+ukâ1Z2s(uk=0), for any integers sâ¥1 and kâ¥2. An explicit algebraic representation of such codes is obtained. This algebraic structure is then used to establish the duals of all cyclic codes. Among others, all self-dual cyclic codes of odd length n over the ring R are determined. Moreover, some examples are provided which produce several optimal codes.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Hai Q. Dinh, Abhay Kumar Singh, Pratyush Kumar, Songsak Sriboonchitta,