Open AccessOn the p ‐Adic Complexity of the Ding‐Helleseth‐Martinsen Binary Sequences
Author(s) -
Xiaoyan Jing,
Zhefeng Xu,
Minghui Yang,
Keqin Feng
Publication year - 2021
Publication title -
chinese journal of electronics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.267
H-Index - 25
eISSN - 2075-5597
pISSN - 1022-4653
DOI - 10.1049/cje.2020.08.016
Subject(s) - gauss , mathematics , quadratic gauss sum , quadratic residue , quadratic equation , gauss sum , exponential function , finite field , exponential sum , binary number , prime (order theory) , binary quadratic form , valuation (finance) , order (exchange) , combinatorics , prime number , discrete mathematics , arithmetic , quadratic function , physics , mathematical analysis , geometry , finance , quantum mechanics , economics
The purpose of this paper is to determine the p ‐adic complexity of the Ding‐Helleseth‐Martinsen (DHM) sequences with period N = 2 q , where q = 5 (mod 8) is a prime number. We firstly use the p ‐adic exponential valuation, cyclotomic numbers of order four, “Gauss periods” and “quadratic Gauss sums” on finite field q , and valued in ℤ N , to determine the p ‐adic complexity of the DHM sequences.