1971•IEEE Transactions on Information TheoryRequires access

Some asymptotically optimal burst-correcting codes and their relation to single-error-correcting Reed-Solomon codes

H. Burton

Abstract

A class of asymptotically optimal burst-correcting codes that are closely related to the Fire codes is defined. The codes are quasi-cyclic as defined by Townsend and Weldon. However, decoding can be accomplished with a very simple algorithm similar to that used for cyclic burst-correcting codes. It is shown that these codes are equivalent to certain Reed-Solomon codes. From this it follows that such Reed-Solomon codes can be easily encoded and decoded without any computations in an extension field.

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Key concepts: Reed–Muller code, Luby transform code, Reed–Solomon error correction, Tornado code, Block code, Linear code, Concatenated error correction code, Expander code