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Binary quadratic residue (QR) codes, which have code rates greater than or equal to 1/2 and generally have large minimum distances, are among the best known codes. This paper considers a modified algebraic decoding algorithm for the (89,45,17) binary QR code that utilizes the Berlekamp-Massey algorithm. It identifies the primary unknown syndromes and provides methods to determine these on a case-by-case...
In order to use Berlekamp-Massey algorithm to decode the (89, 45, 17) binary quadratic residue code, one needs to determine two primary unknown syndromes. In this paper, the authors give some syndrome matrices, so as to calculate one primary unknown syndrome efficiently. This results in a reduction of decoding complexity in terms of CPU time by 35% at least versus the decoder proposed by Truong et...
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