1-generator generalized quasi-cyclic codes over \(\mathbb {Z}_{4}\)

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• 作者：Tingting Wu ; Jian Gao ; Fang-Wei Fu
• 关键词：1 ; generator generalized quasi ; cyclic codes ; New \(\mathbb {Z}_{4}\) ; linear codes ; Gray map ; Good binary nonlinear codes
• 刊名：Cryptography and Communications
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：9
• 期：2
• 页码：291-299
• 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 short paper, we determine the minimal generating set of 1-generator generalized quasi-cyclic codes over \(\mathbb {Z}_{4}\). We also determine their rank and introduce a lower bound for the minimum distance of free 1-generator generalized quasi-cyclic codes. Further, we construct some new \(\mathbb {Z}_{4}\)-linear codes and we obtain some good binary nonlinear codes using the usual Gray map.