On structure and distances of some classes of repeated-root constacyclic codes over Galois rings

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• 作者：Hai Q. Dinh^a ; ^{hdinh@kent.edu} ; Hongwei Liu^b ; ^{hwliu@mail.ccnu.edu.cn} ; Xiu-sheng Liu^c ; ^{lxs6682@163.com} ; Songsak Sriboonchitta^d ; ^{songsakecon@gmail.com}
• 关键词：primary ; 94B15 ; 94B05 ; secondary ; 11T71
• 刊名：Finite Fields and Their Applications
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：43
• 期：Complete
• 页码：86-105
• 全文大小：441 K
• 卷排序：43

文摘

The structure of λ  -constacyclic codes of length 2s2s over the Galois ring GR(2a,m)GR(2a,m) is obtained, for any unit λ   of the form 4z−14z−1, z∈GR(2a,m)z∈GR(2a,m). The duals codes and necessary and sufficient conditions for the existence of a self-dual λ-constacyclic code are provided. Among others, this structure is used to establish the Hamming, homogeneous, and Rosenbloom–Tsfasman distances, and Rosenbloom–Tsfasman weight distribution of all such constacyclic codes.