A note on reducing the computation time for minimum distance and equivalence check of binary linear codes

Abstract

In this paper we show the usability of the Gray code with constant weight words for computing linear combinations of codewords. This can lead to a big improvement of the computation time for finding the minimum distance of a code. We have also considered the usefulness of combinatorial $2$-$(t,k,1)$ designs when there are memory limitations to the number of objects (linear codes in particular) that can be tested for equivalence.