On the Distance Distributions of BCH Codes and Their Duals

Authors:
Ilia Krasikov;Simon Litsyn
Affiliations:
Tel-Aviv University, School of Mathematical Sciences, Ramat-Aviv 69978, Tel-Aviv, Israel and Beit-Berl College, Kfar-Sava, Israel ilia@math.tau.ac.il;Tel-Aviv University, Department of Electrical Engineering–Systems, Ramat-Aviv 69978, Tel-Aviv, Israel litsyn@eng.tau.ac.il
Venue:
Designs, Codes and Cryptography
Year:
2001

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Abstract

Based on new bounds on the values of Krawtchoukpolynomials, we improve earlier known estimates forcomponents of the distance distributions of BCH codes and theirduals. Moreover, we show that if one uses estimates on Krawtchoukpolynomials for bounding the error term in the binomial approximationto the distance distribution of BCH codes, the given results are actuallythe best possible. One of the advantages of the proposed approach isthat it provides estimates with no restrictions on the minimumdistance of the code.