A mass formula for negacyclic codes of length 2 k and some good negacyclic codes over \(\mathbb {Z}_{4}+u\mathbb {Z}_{4}\)
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- 作者：Rama Krishna Bandi ; Maheshanand Bhaintwal ; Nuh Aydin
- 关键词：Codes over \(\mathbb {Z}_{4}+u\mathbb {Z}_{4}\) ; Negacyclic codes ; Cyclic codes ; Repeated root cyclic codes
- 刊名：Cryptography and Communications
- 出版年：2017
- 出版时间：March 2017
- 年：2017
- 卷：9
- 期：2
- 页码：241-272
- 全文大小：
- 刊物类别：Computer Science
- 刊物主题：Data Structures, Cryptology and Information Theory; Coding and Information Theory; Communications Engineering, Networks; Information and Communication, Circuits; Mathematics of Computing;
- 出版者：Springer US
- ISSN：1936-2455
- 卷排序：9
文摘
In this paper, we study negacyclic codes of length 2k over the ring \(R=\mathbb {Z}_{4}+u\mathbb {Z}_{4}\), u2 = 0. We have obtained a mass formula for the number of negacyclic of length 2k over R. We have also determined the number of self-dual negacyclic codes of length 2k over R. This study has been further generalized to negacyclic codes of any even length using discrete Fourier transform approach over R. We have conducted an exhaustive search and obtained some new \(\mathbb {Z}_{4}\)-linear codes with good parameters.