The cross-correlation measure of families of finite binary sequences:\n limiting distributions and minimal values

2016/08/08 by László Mérai, Mérai, László
Computer Science · Engineering · Mathematics · #Cellular Automata and Applications #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #Probability (math.PR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1608.02354

openalex publication_date 2016/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Gyarmati, Mauduit and S 'ark "ozy introduced the cross-correlation measure\n\Φ_k(G) of order k to measure the level of pseudorandom properties of\nfamilies of finite binary sequences. In an earlier paper we estimated the\ncross-correlation measure of a random family of binary sequences. In this\npaper, we sharpen these earlier results by showing that for random families,\nthe cross-correlation measure converges strongly, and so has limiting\ndistribution. We also give sharp bounds to the minimum values of the\ncross-correlation measure, which settles a problem of Gyarmati, Mauduit and\nS 'ark "ozy nearly completely.\n

Related

• The correlation measures of finite sequences: limiting distributions and\n minimum values
• Family complexity and cross-correlation measure for families of binary sequences
• Families of sequences with good family complexity and cross-correlation measure
• Correlation, Linear Complexity, Maximum order Complexity on Families of binary Sequences
• Binary sequences with three-valued cross correlations of different lengths