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More on the distance distribution of BCH codes (1999)
| Venue: | IEEE Trans. Inform. Theory |
| Citations: | 8 - 2 self |
BibTeX
@ARTICLE{Keren99moreon,
author = {Osnat Keren and Simon Litsyn},
title = {More on the distance distribution of BCH codes},
journal = {IEEE Trans. Inform. Theory},
year = {1999},
volume = {45},
pages = {251--255}
}
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Abstract
We derive a new estimate for the error term in the binomial approximation to the distance distribution of BCH codes. This is an improvement on the earlier bounds by Kasami-Fujiwara-Lin, VladutsSkorobogatov, and Krasikov-Litsyn. Keywords: BCH codes, distance distribution 1 Introduction Consider the primitive t-error correcting BCH code of length 2 m \Gamma 1 where 2t \Gamma 2 ! 2 m 2 : It is well known (see e.g. [4, x9.3]) that for such t; the dimension of the code is 2 m \Gamma 1 \Gamma mt. Furthermore, the distance distribution of the code is approximately binomial [4, x9.10] . Namely, the number, b i ; of codewords of weight i is b i = i 2 m \Gamma1 i j 2 mt (1 + E i ); where the error term E i tends to zero when m grows. Moreover, given m, the more i is, the less is the error term. Therefore, it is important to have tight estimates for small values of i. The distance distributions of the BCH code and its extended code of length n = 2 m are related [4, x8.5]. If ...
