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In this paper, we show that a recently proposed algorithm for decoding cyclic codes may be applied efficiently to all binary cyclic codes with t [less than or equal to] 2 and n < 63. This is accomplished by providing structure theorems for the codes in this range and classifying the relevant cases. Index Terms--Cyclic codes, decoding procedure, Grobner bases.

A new lower bound for the distance of cyclic codes is proposed. This bound depends on the defining set of the code, like several other bounds. The proposed bound improves upon the Bose-Chaudhuri-Hocquehghen (BCH) bound and, for some codes, improves upon the Hartmann-Tzeng bound and the Roos bound as well. Index Terms--Bose--Chaudhuri-Hocquehghen (BCH) bound, cyclic codes, Hamming distance, Hartmann-Tzeng bound, Roos bound.

To estimate the weight distribution of a binary linear code, a linear programming approach has been proposed, which leads to the best known values for BCH(255, k). Following that approach, we propose three methods which give tighter estimates. At the same time, we find the distance of the dual of BCH[255, 199, 15]. Index Terms--BCH codes, dual distance, linear programming, undetected error, weight distribution.

In this paper, we show that a recently proposed algorithm for decoding cyclic codes may be applied efficiently to all binary cyclic codes with t ⩽ 2 and n < 63. This is accomplished by providing structure theorems for the codes in this range and classifying the relevant cases. [ABSTRACT FROM AUTHOR]

Presents information on a study which proposed a linear programming approaches to estimate the weight distribution of a binary linear code. Methodology of the study; Results and discussion on the study.