A Heuristic Algorithm for the Construction of Good Linear Codes

In this correspondence, we describe a heuristic method for the construction of linear codes with given parameters n, k, q, and prescribed minimum distance of at least . Our approach is based on a function estimating the probability that a code of dimension and blocklength over is extendable to a code with the given properties. Combining this evaluation function with a search algorithm, we were able to improve 40 entries in the international tables for the best known minimum distance in the cases and found at least two new optimal linear codes.