Showing papers on "BCH code published in 1971"
TL;DR: The iterative algorithm for decoding binary BCH codes presented by Berlekamp and, in an alternative form, by Massey is modified to eliminate inversion.
Abstract: The iterative algorithm for decoding binary BCH codes presented by Berlekamp and, in an alternative form, by Massey is modified to eliminate inversion. Because inversion in a finite field is time consuming and requires relatively complex circuitry, this new algorithm should he useful in practical applications of multiple-error-correcting binary BCH codes.
109 citations
TL;DR: In this paper, majority-logic decoding for the duals of certain primitive polynomial codes is considered and the maximality of Euclidean geometry codes is proved.
Abstract: The class of polynomial codes introduced by Kasami et al. has considerable inherent algebraic and geometric structure. It has been shown that this class of codes and their dual codes contain many important classes of cyclic codes as subclasses, such as BCH codes, Reed-Solomon codes, generalized Reed-Muller codes, projective geometry codes, and Euclidean geometry codes. The purpose of this paper is to investigate further properties of polynomial codes and their duals. First, majority-logic decoding for the duals of certain primitive polynomial codes is considered. Two methods of forming nonorthogonal parity-check sums are presented. Second, the maximality of Euclidean geometry codes is proved. The roots of the generator polynomial of an Euclidean geometry code are specified.
34 citations
TL;DR: 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.
12 citations
Patent•
13 Dec 1971
TL;DR: In this article, Berlekamp's algorithm is restated such that two variables are advantageously combined and a simplified circuit is disclosed for performing the iterations specified by the restated algorithm.
Abstract: Apparatus is disclosed for performing Berlekamp''s algorithm to effect the decoding of binary BCH codes In particular, in accordance with the present invention, Berlekamp''s algorithm is restated such that two variables are advantageously combined and a simplified circuit disclosed for performing the iterations specified by the restated algorithm
8 citations
TL;DR: A new algorithm is given for the decoding of double-error-correcting binary b.h.c. codes that can be rather simply implemented and is particularly suitable for parallel implementation.
Abstract: A new algorithm is given for the decoding of double-error-correcting binary b.c.h. codes. It can be rather simply implemented and is particularly suitable for parallel implementation.
3 citations