On separability of some known nonlinear block codes

A code C is separable if it has a biproper trellis presentation. This trellis simultaneously minimizes the vertex count, the edge count, the cycle rank, and the overall Viterbi decoding complexity. All group codes (including linear codes) are separable. We investigate the separability of nonlinear codes. We give sufficient conditions for a code to be separable and show that some known nonlinear codes are separable. These include Hadamard, Levenshtein, Delsarte-Goethals, Kerdock, and Nordstrom-Robinson codes. All these codes remain separable after every symbol reordering. We show that a conference matrix code C ₉ is not separable, but can be made separable by an appropriate permutation