Loop Transversal Codes for Error Detection

In a loop transversal code, the set of errors is given the structure of a loop transversal to the linear code as a subgroup of the channel. A greedy algorithm for specifying the loop structure, and thus for the construction of loop transversal codes, was discussed by Hummer et al. Apart from some theoretical considerations, the focus was mainly on error correction, in the white noise case constructing codes with odd minimum distance. In this paper, an algorithm to compute loop transversal codes with even minimum distance is given. Some record-breaking codes over a 7-ary alphabet are presented.