Negacyclic codes of length 2/sup s/ over galois rings
Negacyclic codes of length 2/sup s/ over galois rings
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DOI：
10.1109/tit.2005.859284
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发表时间：
2005-12
影响因子：
2.5
通讯作者：
H. Dinh
中科院分区：
文献类型：
--
作者：
H. Dinh
模4整数环上的码已被许多研究者研究。负循环码，使得码的长度n是奇数已经在字母表Zopf 4上被表征，并且此外，已经被推广到字母表是有限交换链环的情况。本文研究了Galois环上长度为2s的无环循环码.完整地得到了Galois环GR（2a，m）上长为2s的无环循环码的结构及其码元的结构.研究了GR（2a，m）上的非循环码的Hamming距离，特别是研究了Zopf 2 a上的非循环码的Hamming距离.在其它更一般的结果中，给出了Zopf 2 a上所有长度为4，8和16的非循环码的Hamming距离.文中还讨论了这类非循环码的重量分布
Codes over the ring of integers modulo 4 have been studied by many researchers. Negacyclic codes such that the length n of the code is odd have been characterized over the alphabet Zopf4, and furthermore, have been generalized to the case of the alphabet being a finite commutative chain ring. In this paper, we investigate negacyclic codes of length 2s over Galois rings. The structure of negacyclic codes of length 2s over the Galois rings GR(2a,m), as well as that of their duals, are completely obtained. The Hamming distances of negacyclic codes over GR(2a,m) in general, and over Zopf2 a in particular are studied. Among other more general results, the Hamming distances of all negacyclic codes over Zopf2 a of length 4,8, and 16 are given. The weight distributions of such negacyclic codes are also discussed