Optimal codebooks achieving the Levenshtein bound from generalized bent functions over \(\mathbb {Z}_{4}\)

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• 作者：Ziling Heng ; Qin Yue
• 关键词：Codebooks ; Signal sets ; Levenstein bounds ; Generalized bent functions
• 刊名：Cryptography and Communications
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：9
• 期：1
• 页码：41-53
• 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

Codebooks (also called signal sets) meeting the Welch bound or the Levenshtein bound are used to distinguish among the signals of different users in CDMA systems. Recently, Zhou, Ding and Li proposed a construction of optimal codebooks based on a set of bent functions satisfying certain conditions over finite fields. In this paper, inspired by the work of Zhou, Ding and Li, we introduce a new construction of codebooks from generalized Boolean bent functions over \(\mathbb {Z}_{4}\). Using this construction, we obtain some optimal codebooks achieving the Levenshtein bound. The codebooks constructed in this paper have parameters (22m+2m, 2m) and a small alphabet size 6. In particular, a set of generalized Boolean bent functions satisfying certain conditions is constructed. As byproducts, some Boolean bent functions are derived.