Generalized Kasami Sequences: The Large Set

2005/11/14 by Xiangyong Zeng, Zeng, Xiangyong, Qingchong Liu +3
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Coding theory and cryptography #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.CR #cs.IT #math.IT

paper · pdf · doi:10.48550/arxiv.cs/0511046

30 pages

arxiv created 2005/11/14 · openalex publication_date 2005/11/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper new binary sequence families F^k of period 2ⁿ-1 are constructed for even n and any k with \rm gcd(k,n)=2 if n/2 is odd or \rm gcd(k,n)=1 if n/2 is even. The distribution of their correlation values is completely determined. These families have maximum correlation 2^n/2+1+1 and family size 2^3n/2+2^n/2 for odd n/2 or 2^3n/2+2^n/2-1 for even n/2. The construction of the large set of Kasami sequences which is exactly the F^k with k=n/2+1 is generalized.

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