Linear complexity of quaternary sequences over Z₄ derived from generalized cyclotomic classes modulo 2p

2016/02/18 by Zhixiong Chen, Chen, Zhixiong, Vladimir Edemskiy +1
Computer Science · Mathematics · #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT) #cs.CR #math.NT

paper · pdf · doi:10.48550/arxiv.1603.05086

arxiv created 2016/02/18 · arxiv updated 2016/03/17

Abstract

We determine the exact values of the linear complexity of 2p-periodic quaternary sequences over Z₄ (the residue class ring modulo 4) defined from the generalized cyclotomic classes modulo 2p in terms of the theory of of Galois rings of characteristic 4, where p is an odd prime. Compared to the case of quaternary sequences over the finite field of order 4, it is more dificult and complicated to consider the roots of polynomials in Z₄[X] due to the zero divisors in Z₄ and hence brings some interesting twists. We answer an open problem proposed by Kim, Hong and Song.

Related

• A kind of quaternary sequences of period 2p^mqⁿ and their linear complexity
• Autocorrelation and Linear Complexity of Quaternary Sequences of Period 2p Based on Cyclotomic Classes of Order Four
• Linear complexity of generalized cyclotomic sequences of order 4 over F_l
• Linear complexity over \mathbbF_q and 2-adic complexity of a class of binary generalized cyclotomic sequences with low-value autocorrelation
• The 4-Adic Complexity of A Class of Quaternary Cyclotomic Sequences with Period 2p