Hamming correlation properties of the array structure of Sidelnikov sequences

Min Kyu Song, Hong Yeop Song

Research output: Contribution to journalArticle

Abstract

In this paper, we investigate the Hamming correlation properties of column sequences from the (q-1)×qd-1q-1 array structure of M-ary Sidelnikov sequences of period qd- 1 for M| q- 1 and d≥ 2. We prove that the proposed set Γ(d) of some column sequences has the maximum non-trivial Hamming correlation upper bounded by the minimum of q-1Md-1 and M-1M[(2d-1)q+1]+q-1M. When M= q- 1 , we show that Γ(d) is optimal with respect to the Singleton bound. The set Γ(d) can be extended to a much larger set Δ(d) by involving all the constant additions of the members of Γ(d) , which is also optimal with respect to the Singleton bound when M= q- 1.

Original languageEnglish
Pages (from-to)2537-2551
Number of pages15
JournalDesigns, Codes, and Cryptography
Volume87
Issue number11
DOIs
Publication statusPublished - 2019 Nov 1

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All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Applied Mathematics

Cite this

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abstract = "In this paper, we investigate the Hamming correlation properties of column sequences from the (q-1)×qd-1q-1 array structure of M-ary Sidelnikov sequences of period qd- 1 for M| q- 1 and d≥ 2. We prove that the proposed set Γ(d) of some column sequences has the maximum non-trivial Hamming correlation upper bounded by the minimum of q-1Md-1 and M-1M[(2d-1)q+1]+q-1M. When M= q- 1 , we show that Γ(d) is optimal with respect to the Singleton bound. The set Γ(d) can be extended to a much larger set Δ(d) by involving all the constant additions of the members of Γ(d) , which is also optimal with respect to the Singleton bound when M= q- 1.",
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Hamming correlation properties of the array structure of Sidelnikov sequences. / Song, Min Kyu; Song, Hong Yeop.

In: Designs, Codes, and Cryptography, Vol. 87, No. 11, 01.11.2019, p. 2537-2551.

Research output: Contribution to journalArticle

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