Waterloo, December 8 - 11, 2017
In this talk we consider covering arrays consisting of discrete logarithms of carefully selected m-sequence elements. Inspired by , we connect the covering array definition for this type of arrays to the value of certain character sums over finite fields. Taking advantage of the balanced way in which the m-sequence elements are distributed, we are able to evaluate these sums. This provides new infinite families of covering arrays of arbitrary strength .
Joint work with L. Moura, B. Stevens and G. Tzanakis.
 C.J. Colbourn, Covering arrays from cyclotomy, Designs, Codes and Cryptography 55 (2010), 201-219.
 L. Moura, G. L. Mullen, D. Panario. Finite field constructions of combinatorial arrays, Designs, Codes and Cryptography 78 (2016), 197-219.
 G. Tzanakis, L. Moura, D. Panario, B. Stevens. Covering arrays from m-sequences and character sums, Designs, Codes and Cryptography 85 (2017), 437-456.