Perfect sequence covering arrays

Raphael Yuster

doi:10.1007/s10623-019-00698-7

Perfect sequence covering arrays

Raphael Yuster

Department of Mathematics

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

Abstract

An (n, k) sequence covering array is a set of permutations of [n] such that each sequence of k distinct elements of [n] is a subsequence of at least one of the permutations. An (n, k) sequence covering array is perfect if there is a positive integer λ such that each sequence of k distinct elements of [n] is a subsequence of precisely λ of the permutations. While relatively close upper and lower bounds for the minimum size of a sequence covering array are known, this is not the case for perfect sequence covering arrays. Here we present new nontrivial bounds for the latter. In particular, for k= 3 we obtain a linear lower bound and an almost linear upper bound.

Original language	English
Pages (from-to)	585-593
Number of pages	9
Journal	Designs, Codes, and Cryptography
Volume	88
Issue number	3
DOIs	https://doi.org/10.1007/s10623-019-00698-7
State	Published - 1 Mar 2020

Bibliographical note

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

Keywords

Completely scrambling set of permutations
Covering array
Directed t-design
Sequence covering array

ASJC Scopus subject areas

Computer Science Applications
Applied Mathematics

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10.1007/s10623-019-00698-7

Cite this

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title = "Perfect sequence covering arrays",

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AB - An (n, k) sequence covering array is a set of permutations of [n] such that each sequence of k distinct elements of [n] is a subsequence of at least one of the permutations. An (n, k) sequence covering array is perfect if there is a positive integer λ such that each sequence of k distinct elements of [n] is a subsequence of precisely λ of the permutations. While relatively close upper and lower bounds for the minimum size of a sequence covering array are known, this is not the case for perfect sequence covering arrays. Here we present new nontrivial bounds for the latter. In particular, for k= 3 we obtain a linear lower bound and an almost linear upper bound.

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KW - Directed t-design

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Perfect sequence covering arrays

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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