On a Class of (δ+αu2)-Constacyclic Codes over Fq[u]/<u4>

Yuan CAO  Yonglin CAO  Jian GAO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E99-A   No.7   pp.1438-1445
Publication Date: 2016/07/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E99.A.1438
Type of Manuscript: PAPER
Category: Cryptography and Information Security
constacyclic code,  dual code,  self-dual code,  finite chain ring,  

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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.