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 | |
| 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