Repeated-root constacyclic codes of prime power length over Fpm[u]〈ua〉 and their duals
| Autor: | Hai Q. Dinh, Songsak Sriboonchitta, Sompong Dhompongsa |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Ring (mathematics) 010102 general mathematics Hamming distance 0102 computer and information sciences Type (model theory) 01 natural sciences Theoretical Computer Science Combinatorics 010201 computation theory & mathematics Discrete Mathematics and Combinatorics Dual polyhedron Isomorphism 0101 mathematics Unit (ring theory) Prime power Hamming code Mathematics |
| Zdroj: | Discrete Mathematics. 339:1706-1715 |
| ISSN: | 0012-365X |
| Popis: | The units of the chain ring R a = F p m u { u a } = F p m + u F p m + ? + u a - 1 F p m are partitioned into a distinct types. It is shown that for any unit ? of Type k , a unit λ of Type k ? can be constructed, such that the class of λ -constacyclic of length p s of Type k ? codes is one-to-one correspondent to the class of ? -constacyclic codes of the same length of Type k via a ring isomorphism. The units of R a of the form ? = ? 0 + u ? 1 + ? + u a - 1 ? a - 1 , where ? 0 , ? 1 , ? , ? a - 1 ? F p m , ? 0 ? 0 , ? 1 ? 0 , are considered in detail. The structure, duals, Hamming and homogeneous distances of ? -constacyclic codes of length p s over R a are established. It is shown that self-dual ? -constacyclic codes of length p s over R a exist if and only if a is even, and in such case, it is unique. Among other results, we discuss some conditions when a code is both α - and β -constacyclic over R a for different units α , β . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect