Repeated-root constacyclic codes of length $ 3\ell^mp^s $

Yan Liu; Minjia Shi; Hai Q. Dinh; Songsak Sriboonchitta

doi:10.3934/amc.2020025

Article Contents

2020, Volume 14, Issue 2: 359-378. Doi: 10.3934/amc.2020025

This issue Previous Article Linear programming bounds for distributed storage codes Next Article Additive Toeplitz codes over

$ \mathbb{F}_{4} $

Repeated-root constacyclic codes of length $ 3\ell^mp^s $

1.
Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematical Sciences, Anhui University, Hefei, Anhui 230601, China
2.
Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam
3.
Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
4.
Centre of Excellence in Econometrics, Faculty of Economics, Chiang Mai University, Chiang Mai 52000, Thailand

^* Corresponding author
^* Corresponding author

Received: July 31, 2018

Revised: April 30, 2016

Early access: September 2019

Published: May 2020

This research is supported by National Natural Science Foundation of China (61672036), Excellent Youth Foundation of Natural Science Foundation of Anhui Province (1808085J20) and Academic fund for outstanding talents in universities (gxbjZD03). H. Q. Dinh and S. Sriboonchitta are grateful to the Centre of Excellence in Econometrics, Chiang Mai University, for partial financial support. This research is partially supported by the Research Administration Center, Chaing Mai University

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Abstract

Let $ p $ be a prime different from 3, and $ \ell $ be an odd prime different from 3 and $ p $. In terms of generator polynomials, structures of constacyclic codes and their duals of length $ 3\ell^mp^s $ over $ \mathbb{F}_q $ are established, where $ q $ is a power of $ p $. We discuss the enumeration of all cyclic codes of length $ 3\cdot2^s\ell^m $, that generalizes the construction of [15] (2016), which is the special case of $ m = 1 $. In addition, as an application, the characterization and enumeration of all linear complementary dual cyclic codes of length $ 6\ell^mp^s $ over $ \mathbb{F}_q $ are obtained.

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Mathematics Subject Classification: Primary: 94B25; Secondary: 05E30.

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