A family of sequences with large size and good correlation property arising from M-ary Sidelnikov sequences of period q^d-1

2010/09/07 by Dae San Kim, Kim, Dae San
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.IT

paper · pdf · doi:10.48550/arxiv.1009.1225

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arxiv created 2010/09/07 · openalex publication_date 2010/09/07 · arxiv updated 2010/09/08 · openalex created_date 2022/09/04 · openalex updated_date 2026/07/28

Abstract

Let q be any prime power and let d be a positive integer greater than 1. In this paper, we construct a family of M-ary sequences of period q-1 from a given M-ary, with M|q-1, Sidelikov sequence of period q^d-1. Under mild restrictions on d, we show that the maximum correlation magnitude of the family is upper bounded by (2d -1) √ q +1 and the asymptotic size, as q→ ∞, of that is \frac (M-1)q^d-1d . This extends the pioneering work of Yu and Gong for d=2 case.

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