On a Class of (δ+αu2)-Constacyclic Codes over Fq[u]/<u4>
Summary :
Let Fq be a finite field of cardinality q, R=Fq[u]/<u4>=Fq+uFq+u2Fq+u3Fq (u4=0) which is a finite chain ring, and n be a positive integer satisfying gcd(q,n)=1. For any $delta,alphain mathbb{F}_{q}^{ imes}$, an explicit representation for all distinct (δ+αu2)-constacyclic codes over R of length n is given, and the dual code for each of these codes is determined. For the case of q=2m and δ=1, all self-dual (1+αu2)-constacyclic codes over R of odd length n are provided.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E99-A No.7 pp.1438-1445
- Publication Date
- 2016/07/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E99.A.1438
- Type of Manuscript
- PAPER
- Category
- Cryptography and Information Security
Authors
Yuan CAO
Hunan University
Yonglin CAO
Shandong University of Technology
Jian GAO
Shandong University of Technology
Keyword
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Yuan CAO, Yonglin CAO, Jian GAO, "On a Class of (δ+αu2)-Constacyclic Codes over Fq[u]/
Abstract: Let Fq be a finite field of cardinality q, R=Fq[u]/<u4>=Fq+uFq+u2Fq+u3Fq (u4=0) which is a finite chain ring, and n be a positive integer satisfying gcd(q,n)=1. For any $delta,alphain mathbb{F}_{q}^{ imes}$, an explicit representation for all distinct (δ+αu2)-constacyclic codes over R of length n is given, and the dual code for each of these codes is determined. For the case of q=2m and δ=1, all self-dual (1+αu2)-constacyclic codes over R of odd length n are provided.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E99.A.1438/_p
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@ARTICLE{e99-a_7_1438,
author={Yuan CAO, Yonglin CAO, Jian GAO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On a Class of (δ+αu2)-Constacyclic Codes over Fq[u]/
year={2016},
volume={E99-A},
number={7},
pages={1438-1445},
abstract={Let Fq be a finite field of cardinality q, R=Fq[u]/<u4>=Fq+uFq+u2Fq+u3Fq (u4=0) which is a finite chain ring, and n be a positive integer satisfying gcd(q,n)=1. For any $delta,alphain mathbb{F}_{q}^{ imes}$, an explicit representation for all distinct (δ+αu2)-constacyclic codes over R of length n is given, and the dual code for each of these codes is determined. For the case of q=2m and δ=1, all self-dual (1+αu2)-constacyclic codes over R of odd length n are provided.},
keywords={},
doi={10.1587/transfun.E99.A.1438},
ISSN={1745-1337},
month={July},}
Copy
TY - JOUR
TI - On a Class of (δ+αu2)-Constacyclic Codes over Fq[u]/
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1438
EP - 1445
AU - Yuan CAO
AU - Yonglin CAO
AU - Jian GAO
PY - 2016
DO - 10.1587/transfun.E99.A.1438
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E99-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 2016
AB - Let Fq be a finite field of cardinality q, R=Fq[u]/<u4>=Fq+uFq+u2Fq+u3Fq (u4=0) which is a finite chain ring, and n be a positive integer satisfying gcd(q,n)=1. For any $delta,alphain mathbb{F}_{q}^{ imes}$, an explicit representation for all distinct (δ+αu2)-constacyclic codes over R of length n is given, and the dual code for each of these codes is determined. For the case of q=2m and δ=1, all self-dual (1+αu2)-constacyclic codes over R of odd length n are provided.
ER -
English
