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Repeated-root constacyclic codes of length 6lmpn.
- Source :
- Advances in Mathematics of Communications; Oct2023, Vol. 17 Issue 5, p1-27, 27p
- Publication Year :
- 2023
-
Abstract
- Let $ \mathbb{F}_{q} $ be a finite field with character $ p $. In this paper, the multiplicative group $ \mathbb{F}_{q}^{*} = \mathbb{F}_{q}\setminus\{0\} $ is decomposed into a mutually disjoint union of $ \gcd(6l^mp^n,q-1) $ cosets over subgroup $ <\xi^{6l^mp^n}> $, where $ \xi $ is a primitive element of $ \mathbb{F}_{q} $. Based on the decomposition, the structure of constacyclic codes of length $ 6l^mp^n $ over finite field $ \mathbb{F}_{q} $ and their duals is established in terms of their generator polynomials, where $ p\neq{3} $ and $ l\neq{3} $ are distinct odd primes, $ m $ and $ n $ are positive integers. In addition, we determine the characterization and enumeration of all linear complementary dual(LCD) negacyclic codes and self-dual constacyclic codes of length $ 6l^mp^n $ over $ \mathbb{F}_{q} $. [ABSTRACT FROM AUTHOR]
- Subjects :
- POLYNOMIALS
INTEGERS
FINITE fields
Subjects
Details
- Language :
- English
- ISSN :
- 19305346
- Volume :
- 17
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Advances in Mathematics of Communications
- Publication Type :
- Academic Journal
- Accession number :
- 167382482
- Full Text :
- https://doi.org/10.3934/amc.2021044