Improved Decoding Algorithm of BD-LRPC Codes

Abstract: A Bounded-Degree Low-Rank Parity-Check (BD-LRPC) code is a rank-metric code that admits a parity-check matrix whose support is generated by a set of powers of an element. This specific structure of the parity-check matrix was employed to enhance the first phase of the decoding algorithm through the expansion of the syndrome support. However, this expansion decreases the probability of recovering the error support in the second phase of the decoding algorithm. This paper introduces a novel method based on successive intersections to recover the error support. This method offers two key advantages: it increases the probability of successful decoding and enables the decoding of a greater number of errors.