Repeated-root constacyclic codes of length $ 6lp^s $

Tingting Wu; Li Liu; Lanqiang Li; Shixin Zhu

doi:10.3934/amc.2020051

Article Contents

2021, Volume 15, Issue 1: 167-189. Doi: 10.3934/amc.2020051

This issue Previous Article Some properties of the cycle decomposition of WG-NLFSR Next Article Properties of sets of subspaces with constant intersection dimension

Repeated-root constacyclic codes of length $ 6lp^s $

School of Mathematics, Hefei University of Technology, Hefei 230601, China

^* Corresponding author: Li Liu
^* Corresponding author: Li Liu

Received: April 2019

Revised: September 2019

Early access: January 2020

Published: February 2021

This research is supported in part by the National Natural Science Foundation of China under Project 11871187 and Project 61772168.

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Abstract

Let $ \mathbb{F}_{q} $ be a finite field with character $ p $ and $ p\neq{3},l\neq{3} $ be different odd primes. In this paper, we study constacyclic codes of length $ 6lp^s $ over finite field $ \mathbb{F}_{q} $. The generator polynomials of all constacyclic codes and their duals are obtained. Moreover, we give the characterization and enumeration of linear complementary dual (LCD) and self-dual constacyclic codes of length $ 6lp^s $ over $ \mathbb{F}_{q} $.

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Mathematics Subject Classification: Primary: 94B05, 11T71; Secondary: 94B15.

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Table 1. LCD cyclic codes

$ p $	l	length	dimension	minimum distance
$ 5 $	$ 29 $	$ 870 $	$ 785 $	3
$ 5 $	$ 29 $	$ 870 $	$ 780 $	4
$ 5 $	$ 29 $	$ 870 $	$ 10 $	116
$ 5 $	$ 29 $	$ 870 $	$ 5 $	174
$ 11 $	$ 7 $	$ 462 $	$ 374 $	4
$ 11 $	$ 7 $	$ 462 $	$ 242 $	6
$ 11 $	$ 7 $	$ 462 $	$ 165 $	8

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Table 2. LCD negacyclic codes

$ p $	l	length	dimension	minimum distance
$ 11 $	5	$ 330 $	$ 286 $	3
$ 11 $	5	$ 330 $	$ 264 $	4
$ 11 $	5	$ 330 $	$ 242 $	5
$ 11 $	5	$ 330 $	$ 176 $	7
$ 11 $	5	$ 330 $	$ 154 $	8
$ 13 $	11	$ 858 $	$ 594 $	3
$ 13 $	11	$ 858 $	$ 550 $	4
$ 37 $	5	$ 1110 $	$ 814 $	3
$ 37 $	5	$ 1110 $	$ 666 $	5
$ 37 $	5	$ 1110 $	$ 592 $	6
$ 37 $	5	$ 1110 $	$ 296 $	10
$ 37 $	5	$ 1110 $	$ 148 $	12

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Table 3. self-dual negacyclic codes

$ p $	l	length	dimension	minimum distance
$ 13 $	5	$ 390 $	$ 195 $	6
$ 13 $	11	$ 858 $	$ 429 $	6
$ 13 $	19	$ 1482 $	$ 741 $	6
$ 37 $	5	$ 1110 $	$ 555 $	6

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