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20.02.2018 | Ausgabe 11/2018

# Covering arrays of strength three from extended permutation vectors

Zeitschrift:
Designs, Codes and Cryptography > Ausgabe 11/2018
Autoren:
Jose Torres-Jimenez, Idelfonso Izquierdo-Marquez
Wichtige Hinweise
Communicated by D. Panario.

## Abstract

A covering array $$\text{ CA }(N;t,k,v)$$ is an $$N\times k$$ array such that in every $$N\times t$$ subarray each possible t-tuple over a v-set appears as a row of the subarray at least once. The integers t and v are respectively the strength and the order of the covering array. Let v be a prime power and let $${\mathbb {F}}_v$$ denote the finite field with v elements. In this work the original concept of permutation vectors generated by a $$(t-1)$$-tuple over $${\mathbb {F}}_v$$ is extended to vectors generated by a t-tuple over $${\mathbb {F}}_v$$. We call these last vectors extended permutation vectors (EPVs). For every prime power v, a covering perfect hash family $$\text{ CPHF }(2;v^2-v+3,v^3,3)$$ is constructed from EPVs given by subintervals of a linear feedback shift register sequence over $${\mathbb {F}}_v$$. When $$v\in \{7,9,11,13,16,17,19,23,25\}$$ the covering array $$\text{ CA }(2v^3-v;3,v^2-v+3,v)$$ generated by $$\text{ CPHF }(2;v^2-v+3,v^3,3)$$ has less rows than the best-known covering array with strength three, $$v^2-v+3$$ columns, and order v. CPHFs formed by EPVs are also constructed using simulated annealing; in this case the results improve the size of eighteen covering arrays of strength three.

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