Codebooks from generalized bent ℤ₄-valued quadratic forms

2019/05/21 by Yanfeng Qi, Sihem Mesnager, Qi, Yanfeng +3
Computer Science · Engineering · #Coding theory and cryptography #Cryptographic Implementations and Security #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1905.08834

openalex publication_date 2019/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Codebooks with small inner-product correlation have application in unitary space-time modulations, multiple description coding over erasure channels, direct spread code division multiple access communications, compressed sensing, and coding theory. It is interesting to construct codebooks (asymptotically) achieving the Welch bound or the Levenshtein bound. This paper presented a class of generalized bent ℤ₄-valued quadratic forms, which contain functions of Heng and Yue (Optimal codebooks achieving the Levenshtein bound from generalized bent functions over ℤ₄. Cryptogr. Commun. 9(1), 41-53, 2017). By using these generalized bent ℤ₄-valued quadratic forms, we constructs optimal codebooks achieving the Levenshtein bound. These codebooks have parameters (2^2m+2^m,2^m) and alphabet size 6.

Related

• Asymptotically optimal codebooks derived from generalised bent functions
• Nearly optimal codebooks based on generalized Jacobi sums
• Two constructions of asymptotically optimal codebooks via the trace functions
• Linear Codes with Two or Three Weights From Quadratic Bent Functions
• Six constructions of asymptotically optimal codebooks via the character sums