Hamming correlation properties of the array structure of Sidelnikov sequences

作     者：Song, Min Kyu Song, Hong-Yeop 

作者机构：Yonsei Univ Sch Elect & Elect Engn Yonsei Rho 50 Seoul South Korea 

出 版 物：《DESIGNS CODES AND CRYPTOGRAPHY》 (设计、编码与密码学)

年 卷 期：2019年第87卷第11期

页      面：2537-2551页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

基　　金：National Research Foundation of Korea (NRF) - Korea government (MSIP) [2017R1A2B4011191] 

主　　题：Codes for FHMA Sequences Hamming correlation Sidelnikov sequences Array structure 

摘      要：In this paper, we investigate the Hamming correlation properties of column sequences from the (q - 1) x q(d)-1/q-1 array structure of M-ary Sidelnikov sequences of period q(d) - 1 for M vertical bar q - 1 and d = 2. We prove that the proposed set Gamma (d) of some column sequences has the maximum non-trivial Hamming correlation upper bounded by the minimum of q-1/Md - 1 and M-1/M[(2d - 1)root q + 1] + q-1/M. When M = q - 1, we show that Gamma (d) is optimal with respect to the Singleton bound. The set Gamma (d) can be extended to a much larger set Delta(d) by involving all the constant additions of the members of Gamma (d), which is also optimal with respect to the Singleton bound when M = q - 1.