# American Institute of Mathematical Sciences

doi: 10.3934/amc.2021044
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## Repeated-root constacyclic codes of length 6lmpn

 1 School of Mathematics, Hefei University of Technology, Hefei 230009, China 2 Intelligent Interconnected Systems Laboratory of Anhui Province Hefei, China 3 School of Science, Anhui Agricultural University, Hefei 230036, Anhui, China

* Corresponding author: Li Liu

Received  March 2021 Early access September 2021

Fund Project: This research is supported in part by the National Natural Science Foundation of China under Project 61772168, 12001002, the fundamental Research Funds for the Central Universities under Project PA2021KCPY0040 and the Natural Science Foundation of Anhui Province under Project 2108085QA06, 2008085QA04, 2108085QA03

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 $\mathbb{F}_{q}$.

Citation: Tingting Wu, Shixin Zhu, Li Liu, Lanqiang Li. Repeated-root constacyclic codes of length 6lmpn. Advances in Mathematics of Communications, doi: 10.3934/amc.2021044
##### References:

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##### References:
LCD negacyclic codes1
 q l m length dimension minimum distance 5 7 2 1470 1460 2 5 7 2 1470 1050 6 5 7 2 1470 60 84 5 17 1 510 190 17 5 19 1 570 110 38 13 5 2 1950 1404 5 13 5 2 1950 858 10 13 5 2 1950 26 125 25 11 1 330 320 2 25 11 1 330 260 6 25 11 1 330 120 14
 q l m length dimension minimum distance 5 7 2 1470 1460 2 5 7 2 1470 1050 6 5 7 2 1470 60 84 5 17 1 510 190 17 5 19 1 570 110 38 13 5 2 1950 1404 5 13 5 2 1950 858 10 13 5 2 1950 26 125 25 11 1 330 320 2 25 11 1 330 260 6 25 11 1 330 120 14
LCD negacyclic codes2
 q l length dimension minimum distance 7 11 462 224 13 7 11 462 154 18 7 13 546 364 6 7 13 546 196 17 7 13 546 168 22 7 31 1302 1288 2 7 31 1302 14 93 11 19 1254 1078 6 11 19 1254 308 24 11 19 1254 154 55
 q l length dimension minimum distance 7 11 462 224 13 7 11 462 154 18 7 13 546 364 6 7 13 546 196 17 7 13 546 168 22 7 31 1302 1288 2 7 31 1302 14 93 11 19 1254 1078 6 11 19 1254 308 24 11 19 1254 154 55
self-dual negacyclic codes
 q l m length dimension minimum distance 13 5 2 1950 975 6 5 7 2 1470 735 8 5 11 1 330 165 8 5 17 1 510 255 8 5 19 1 570 285 8 5 23 1 690 345 8
 q l m length dimension minimum distance 13 5 2 1950 975 6 5 7 2 1470 735 8 5 11 1 330 165 8 5 17 1 510 255 8 5 19 1 570 285 8 5 23 1 690 345 8
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