Journal ArticleDOI
A note on the decoding of double-error-correcting binary BCH codes of primitive length (Corresp.)
TLDR
In this correspondence a complete decoding algorithm for double-error-correcting binary BCH codes of length n = 2^m - 1 is introduced, based on the step-by-step decoding algorithm introduced by Prange and the decoding algorithms introduced by Meggitt, which makes use of the cyclic properties of the code.Abstract:
In this correspondence a complete decoding algorithm for double-error-correcting binary BCH codes of length n = 2^m - 1 is introduced. It corrects all patterns of one and two errors and all patterns of three errors that belong to cosets that have a coset leader of weight three. This algorithm is based on the step-by-step decoding algorithm introduced by Prange and the decoding algorithm introduced by Meggitt, which makes use of the cyclic properties of the code. A comparison between this method and previously existing ones is also given.read more
Citations
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Journal ArticleDOI
Complete decoding of triple-error-correcting binary BCH codes
J. van der Horst,T. Berger +1 more
TL;DR: An extensive study of binary triple-error-correcting codes of primitive length n = 2^{m} - 1 is reported that results in a complete decoding algorithm whenever the maximum coset weight W_{max} is five.
Journal ArticleDOI
Decoding beyond the BCH bound (Corresp.)
TL;DR: In this correspondence, a decoding algorithm to decode beyond the BCH bound is introduced and gives a complete minimum distance decoding for any cyclic code.
Journal ArticleDOI
High-speed hardware decoder for double-error-correcting binary BCH codes
Shyue-Win Wei,Che-Ho Wei +1 more
TL;DR: A new hardware decoder for double-error-correcting binary BCH codes of primitive length, based on a modified step-by-step decoding algorithm, which is suitable for long block codes working at high data rates.
Journal ArticleDOI
A complete decoding algorithm for double-error-correcting primitive binary BCH codes of odd m
TL;DR: Since this code is a quasi-perfect code [l], a complete decoding algorithm should be capable of correcting 2”Pk error vectors that include all of the error vectors of weight equal to or less than 2 and some error vector of weight 3.
References
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Journal ArticleDOI
Cyclic decoding procedures for Bose- Chaudhuri-Hocquenghem codes
TL;DR: New general error-correction procedures for class of codes known as Bose-Chaudhuri-Hocquenghem codes are presented and it is shown that these procedures are efficient in time required for error-Correction, and that they can be implemented with relatively simple electronic circuits.
Journal ArticleDOI
Two-error correcting Bose-Chaudhuri codes are quasi-perfect
TL;DR: It is shown that all two-error correcting Bose-Chaudhuri codes are close-packed and therefore optimum, and a method is given for finding cosets of large weight in t > 2- error correcting BOSE-Choudhuri code, which suggests that no other nontrivial codes areClose-packed.
Journal ArticleDOI
Decoding beyond the BCH bound (Corresp.)
TL;DR: In this correspondence, a decoding algorithm to decode beyond the BCH bound is introduced and gives a complete minimum distance decoding for any cyclic code.
Journal ArticleDOI
Error correcting codes for correcting bursts of errors
TL;DR: It is observed that the codes of Abramson, Melas and others are essentially described by the characteristic equation that a certain matrix satisfies and it is found that transformations of these codes are possible provided that the characteristic equations is preserved.