


























Our main technical result is that, in the coset leader graph of a linear binary code of block length n, the metric balls spanned by constant-weight vectors grow exponentially slower than those in $\{0,1\}^n$. Following the approach of Friedman and Tillich (2006), we use this fact to improve on the first linear programming bound on the rate of LDPC codes, as the function of their minimal distance. This improvement, combined with the techniques of Ben-Haim and Lytsin (2006), improves the rate vs distance bounds for LDPC codes in a significant sub-range of relative distances.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。