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Cryptography and Communications

Erschienen in:

15.06.2019

Binary and ternary sequences with a few cross correlations

verfasst von: Yansheng Wu, Qin Yue, Xueying Shi, Xiaomeng Zhu

Erschienen in: Cryptography and Communications | Ausgabe 3/2020

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Abstract

Let m be a positive integer, r ≡ 1 (mod 3) be a prime number, and the order of p modulo r^m be \(\frac {\phi (r^{m})}3\), where ϕ is the Euler function. Let \(q=p^{\frac {\phi (r^{m})}3}\) and \(d=\frac {q-1}{r^{m}}\). We investigate the cross correlation distribution between a p-ary m-sequence and its d-decimated sequences. In this paper, we deal with the cases of p = 2 and p = 3. Our results show that the binary sequences have two-valued cross correlations and the ternary sequences have at most three-valued cross correlations, see Theorems 3.2 and 4.2. As a byproduct, we also explicitly compute the Gauss periods \(\eta _{0}^{(\frac {q-1}{r^{m}},q)}\).

Vorheriger Artikel Properties of tight frames that are regular schemes

Nächster Artikel Partially APN Boolean functions and classes of functions that are not APN infinitely often

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Titel: Binary and ternary sequences with a few cross correlations
verfasst von: Yansheng Wu
Qin Yue
Xueying Shi
Xiaomeng Zhu
Publikationsdatum: 15.06.2019
Verlag: Springer US
Erschienen in: Cryptography and Communications / Ausgabe 3/2020
Print ISSN: 1936-2447
Elektronische ISSN: 1936-2455
DOI: https://doi.org/10.1007/s12095-019-00376-4

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