A heuristic algorithm for the construction of good linear codes

Titelangaben

Zwanzger, Johannes:
A heuristic algorithm for the construction of good linear codes.
In: IEEE Transactions on Information Theory. Bd. 54 (2008) Heft 5 . - S. 2388-2392.
ISSN 0018-9448
DOI: https://doi.org/10.1109/TIT.2008.920323

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Abstract

In this correspondence, we describe a heuristic method for the construction of linear codes with given parameters n, k, q, and a prescribed minimum distance of at least d. Our approach is based on a function estimating the probability that a code of dimension k and blocklength n' < n over GF( q) 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 q = 2, 5, 7, 9 and found at least two new optimal linear codes.