Trellis complexity and pseudoredundancy of relative two-weight codes

Abstract

Relative two-weight codes have been studied due to their applications to wiretap channel and secret sharing. It has been shown that these codes form a large family, which includes dual Hamming codes and subcodes of punctured Reed-Muller codes as special instances. This work studies the properties of relative two-weight codes with regard to efficient decoding. More specifically, the trellis complexity, which determines the complexity of Viterbi algorithm based decoding and pseudoredundancy that measures the performance and complexity of linear programming decoding are studied for relative two-weight codes. Separating properties of these codes have been identified and proved first. Based on the results of separating properties, the trellis complexity of binary relative two-weight codes is fully determined. An upper bound on the pseudoredundancy of binary relative two-weight codes is derived.