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Designs, Codes and Cryptography

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27.04.2019

Hamming correlation properties of the array structure of Sidelnikov sequences

verfasst von: Min Kyu Song, Hong-Yeop Song

Erschienen in: Designs, Codes and Cryptography | Ausgabe 11/2019

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Abstract

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

Vorheriger Artikel Matrix theory for minimal trellises

Nächster Artikel A new Gaussian sampling for trapdoor lattices with arbitrary modulus

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Titel: Hamming correlation properties of the array structure of Sidelnikov sequences
verfasst von: Min Kyu Song
Hong-Yeop Song
Publikationsdatum: 27.04.2019
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 11/2019
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-019-00636-7

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Hamming correlation properties of the array structure of Sidelnikov sequences

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