Name
Abstract | ||
|---|---|---|
Let p ź 3 be any prime and l ź 3 be any odd prime with gcd ź ( p , l ) = 1 . The multiplicative group F q * = { ź } can be decomposed into mutually disjoint union of gcd ź ( q - 1 , 3 l p s ) cosets over the subgroup { ź 3 l p s } , where ź is a primitive ( q - 1 ) th root of unity. We classify all repeated-root constacyclic codes of length 3 l p s over the finite field F q into some equivalence classes by this decomposition, where q = p m , s and m are positive integers. According to these equivalence classes, we explicitly determine the generator polynomials of all repeated-root constacyclic codes of length 3 l p s over F q and their dual codes. Self-dual cyclic codes of length 3 l p s over F q exist only when p = 2 . We give all self-dual cyclic codes of length 3 ź 2 s l over F 2 m and their enumeration. We also determine the minimum Hamming distance of these codes when gcd ź ( 3 , q - 1 ) = 1 and l = 1 . |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1016/j.ffa.2016.08.005 | Finite Fields and Their Applications |
Keywords | Field | DocType |
94B05,11T71 | Prime (order theory),Integer,Discrete mathematics,Combinatorics,Finite field,Multiplicative group,Algebra,Polynomial code,Root of unity,Hamming distance,Coset,Mathematics | Journal |
Volume | Issue | ISSN |
42 | C | 1071-5797 |
Citations | PageRank | References |
1 | 0.36 | 7 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Li Liu | 1 | 9 | 1.55 |
| Lanqiang Li | 2 | 1 | 0.70 |
| Xiaoshan Kai | 3 | 3 | 1.11 |
| Shixin Zhu | 4 | 216 | 37.61 |