Almost supplementary difference sets and quaternary sequences with optimal autocorrelation

J. A. Armario; D. L. Flannery

doi:10.1007/s12095-019-00418-x

Almost supplementary difference sets and quaternary sequences with optimal autocorrelation

J. A. Armario
, D. L. Flannery

Mathematics

University of Sevilla

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

3 Citations (Scopus)

Abstract

We introduce almost supplementary difference sets (ASDS). For odd m, certain ASDS in ℤ_m that have amicable incidence matrices are equivalent to quaternary sequences of odd length m with optimal autocorrelation. As one consequence, if 2m − 1 is a prime power, or m ≡ 1 mod 4 is prime, then ASDS of this kind exist. We also explore connections to optimal binary sequences and group cohomology.

Original language	English
Pages (from-to)	757-768
Number of pages	12
Journal	Cryptography and Communications
Volume	12
Issue number	4
DOIs	https://doi.org/10.1007/s12095-019-00418-x
Publication status	Published - 1 Jul 2020

Keywords

Array
Autocorrelation
Cocycle
Difference set
Quasi-orthogonal
Sequence

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10.1007/s12095-019-00418-x

Cite this

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abstract = "We introduce almost supplementary difference sets (ASDS). For odd m, certain ASDS in ℤm that have amicable incidence matrices are equivalent to quaternary sequences of odd length m with optimal autocorrelation. As one consequence, if 2m − 1 is a prime power, or m ≡ 1 mod 4 is prime, then ASDS of this kind exist. We also explore connections to optimal binary sequences and group cohomology.",

keywords = "Array, Autocorrelation, Cocycle, Difference set, Quasi-orthogonal, Sequence",

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AU - Flannery, D. L.

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N2 - We introduce almost supplementary difference sets (ASDS). For odd m, certain ASDS in ℤm that have amicable incidence matrices are equivalent to quaternary sequences of odd length m with optimal autocorrelation. As one consequence, if 2m − 1 is a prime power, or m ≡ 1 mod 4 is prime, then ASDS of this kind exist. We also explore connections to optimal binary sequences and group cohomology.

AB - We introduce almost supplementary difference sets (ASDS). For odd m, certain ASDS in ℤm that have amicable incidence matrices are equivalent to quaternary sequences of odd length m with optimal autocorrelation. As one consequence, if 2m − 1 is a prime power, or m ≡ 1 mod 4 is prime, then ASDS of this kind exist. We also explore connections to optimal binary sequences and group cohomology.

KW - Array

KW - Autocorrelation

KW - Cocycle

KW - Difference set

KW - Quasi-orthogonal

KW - Sequence

UR - https://www.scopus.com/pages/publications/85077715411

U2 - 10.1007/s12095-019-00418-x

DO - 10.1007/s12095-019-00418-x

M3 - Article

AN - SCOPUS:85077715411

SN - 1936-2447

VL - 12

SP - 757

EP - 768

JO - Cryptography and Communications

JF - Cryptography and Communications

IS - 4

ER -

Almost supplementary difference sets and quaternary sequences with optimal autocorrelation

Abstract

Keywords

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