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A note on optimum burst-error-correcting codes | IEEE Journals & Magazine | IEEE Xplore

A note on optimum burst-error-correcting codes


Abstract:

A detailed study has been made of a certain class of systematic binary error-correcting codes that will correct the error bursts typical of some digital channels. These c...Show More

Abstract:

A detailed study has been made of a certain class of systematic binary error-correcting codes that will correct the error bursts typical of some digital channels. These codes--generalizations of codes discovered by Abramson and Melas--are cyclic codes designed to correct any single burst of errors pern-digit word provided that the width of the burst (regarded cyclically) does not exceed a certain number of digits,b. Moreover, these codes are optimum in the sense that they employ the minimum number of redundant digits theoretically possible for a cyclic code with given values ofnandb. A cyclic code is completely characterized by its generator polynomialg(x), hence, the properties of the code can be determined by analysis of the correspondingg(x). Necessary and sufficient conditions ong(x)have been formulated for the corresponding cyclic code to be an optimum burst-bcorrecting code. These conditions have been formulated into a series of tests that can be carried out (in principle) on anyg(x). All optimum burst-bcyclic codes withn < 2^{12}andb < 6have been found in this way and their generators are tabulated in the paper. In all, 98 codes are listed (not counting reciprocals) forb = 3andb = 4; it was shown that no optimum codes exist forb = 5within the limits stated. Practical codes forb \geq 6will probably be nonoptimum codes because of the extreme word lengths required for optimum ones.
Published in: IRE Transactions on Information Theory ( Volume: 8, Issue: 1, January 1962)
Page(s): 39 - 42
Date of Publication: 06 January 2003

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