标题:Explicit representation and enumeration of repeated-root (δ + αu2)-Constacyclic Codes over F2m[u]/⟨u2?⟩
作者:Cao Y.; Cao Y.; Dinh H.Q.; Bag T.; Yamaka W.
作者机构:[Cao, Y] School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255091, China, Hubei Key Laboratory of Applied Mathematics, Fa 更多
通讯作者:Dinh, HQ(dinhquanghai@tdtu.edu.vn)
通讯作者地址:[Dinh, H.Q] Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang UniversityViet Nam;
来源:IEEE Access
出版年:2020
卷:8
页码:55550-55562
DOI:10.1109/ACCESS.2020.2981453
关键词:finite chain ring; linear code; repeated-root code; Type 2 constacyclic code
摘要:Let F2m be a finite field of 2m elements, λ and k be integers satisfying λ,k ≥ 2 and denote R= F2m[u]/‹ u2λ ›. Let δ,α F2m×. For any odd positive integer n, we give an explicit representation and enumeration for all distinct (δ +α u2)-constacyclic codes over R of length 2kn, and provide a clear formula to count the number of all these codes. In particular, we conclude that every (δ +α u2)-constacyclic code over R of length 2kn is an ideal generated by at most 2 polynomials in the ring R[x]/‹ x2kn-(δ +α u2)›. As an example, we listed all 135 distinct (1+u2)-constacyclic codes of length 4 over F2[u]/‹ u4›, and apply our results to determine all 11 self-dual codes among them. © 2013 IEEE.
收录类别:SCOPUS
Scopus被引频次:2
资源类型:期刊论文
原文链接:https://www.scopus.com/inward/record.uri?eid=2-s2.0-85082832767&doi=10.1109%2fACCESS.2020.2981453&partnerID=40&md5=faca7e431ae7bdc13ed6a0f44ccb94b7
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