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[Cao, Y] School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255091, China, Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, 410114, China;[ Cao, Y] School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255091, China;[ Dinh, H.Q] Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, 700000, Viet Nam, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, 700000, Viet Nam;[ Bag, T] Department of Mathematics, Indian Institute of Technology Patna, Patna, 801103, India;[ Yamaka, W] Centre of Excellence in Econometrics, Chiang Mai University, Chiang Mai, 50200, Thailand 收起 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
