A lower bound on the 2-adic complexity of Ding-Helleseth generalized cyclotomic sequences of period pⁿ

2017/04/18 by Yuhua Sun, Sun, Yuhua, Qiang Wang +5
Computer Science · Engineering · #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1704.05544

openalex publication_date 2017/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be an odd prime, n a positive integer and g a primitive root of pn. Suppose Di(pn)=\g2s+i|s=0,1,2,⋯,\frac(p-1)pn-12\, i=0,1, is the generalized cyclotomic classes with Zpn∗=D0∪ D1. In this paper, we prove that Gauss periods based on D0 and D1 are both equal to 0 for n≥2. As an application, we determine a lower bound on the 2-adic complexity of a class of Ding-Helleseth generalized cyclotomic sequences of period pn. The result shows that the 2-adic complexity is at least pn-pn-1-1, which is larger than (N+1)/(2), where N=pn is the period of the sequence.

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