Hamming correlation properties of the array structure of Sidelnikov sequences

Min Kyu Song; Hong Yeop Song

doi:10.1007/s10623-019-00636-7

Hamming correlation properties of the array structure of Sidelnikov sequences

Min Kyu Song, Hong Yeop Song

Department of Electrical and Electronic Engineering

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 q^d- 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 language	English
Pages (from-to)	2537-2551
Number of pages	15
Journal	Designs, Codes, and Cryptography
Volume	87
Issue number	11
DOIs	https://doi.org/10.1007/s10623-019-00636-7
Publication status	Published - 2019 Nov 1

Bibliographical note

Funding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2017R1A2B4011191).

Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.

All Science Journal Classification (ASJC) codes

Computer Science Applications
Applied Mathematics

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title = "Hamming correlation properties of the array structure of Sidelnikov sequences",

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.",

author = "Song, {Min Kyu} and Song, {Hong Yeop}",

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N1 - Funding Information: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2017R1A2B4011191). Publisher Copyright: © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

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N2 - 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.

AB - 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

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