2020/04/29 by Doğan, Kenan, Şahin, Murat, Yayla, Oğuz
Computer Science · Engineering · #11K45 #94A55 #94A60 #Coding theory and cryptography #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT) #graph theory and CDMA systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2004.13938
openalex publication_date 2020/04/29 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
In this paper we study pseudorandomness of a family of sequences in terms of two measures, the family complexity (f-complexity) and the cross-correlation measure of order ℓ. We consider sequences not only on binary alphabet but also on k-symbols (k-ary) alphabet. We first generalize some known methods on construction of the family of binary pseudorandom sequences. We prove a bound on the f-complexity of a large family of binary sequences of Legendre-symbols of certain irreducible polynomials. We show that this family as well as its dual family have both a large family complexity and a small cross-correlation measure up to a rather large order. Next, we present another family of binary sequences having high f-complexity and low cross-correlation measure. Then we extend the results to the family of sequences on k-symbols alphabet.