t-CIS codes over GF (p) and orthogonal arrays

Abstract

We first show that orthogonal arrays over GF(p) can be explicitly constructed from t-CIS codes over GF(p), where t-CIS codes are CIS codes of order t >= 2. With this motivation, we are interested in developing methods of constructing t-CIS codes over GF(p). We present two types of constructions; the first one is a "t-extension method" which is finding t-CIS codes over GF(p) of length tn from given (t - 1)-CIS codes over GF(p) of length (t - 1)n for t > 2, and the second one is a "building-up type construction" which is finding t-CIS codes over GF(p) of length t (n + 1) from given t-CIS codes over GF(p) of length tn. Furthermore, we find a criterion for checking equivalence of t-CIS codes over GF(p). We find inequivalent t-CIS codes over GF(p) of length n for t = 3, 4, n = 9, 12, 16, and p = 3, 5, 7 using our construction and criterion, and corresponding orthogonal arrays are found. We point out that 171t-CIS codes we found are optimal codes. (C) 2016 Elsevier B.V. All rights reserved.