On the minimum distance of some families of ℤ2k-linear codes

Abstract

With the help of a computer, we obtain the minimum distance of some codes belonging to two families of ℤ2k-linear codes: the first is the generalized Kerdock codes which aren't as good as the best linear codes and the second is the Hensel lift of quadratic residue codes. In the latter, we found new codes with same minimum distances as the best linear codes of same length and same cardinality. We give a construction of binary codes starting with a ℤ2k-linear code and adding cosets to it, increasing its cardinality and keeping the same minimum distance. This construction allows to derive a non trivial upper bound on cardinalities of ℤ2k-linear Codes. © Springer-Verlag Berlin Heidelberg 2003.