2012/12/22 by Yun Fan, San Ling, Fan, Yun +7
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Algorithms and Data Compression #Coding theory and cryptography #DNA and Biological Computing #cs.IT #math.IT #msc:82B26 #msc:94B65 #msc:94B99
paper · pdf · doi:10.48550/arxiv.1212.5679
arxiv created 2012/12/22 · arxiv updated 2012/12/27
Cumulative weight enumerators of random linear codes are introduced, their asymptotic properties are studied, and very sharp thresholds are exhibited; as a consequence, it is shown that the asymptotic Gilbert-Varshamov bound is a very sharp threshold point for the density of the linear codes whose relative distance is greater than a given positive number. For arbitrary random codes, similar settings and results are exhibited; in particular, the very sharp threshold point for the density of the codes whose relative distance is greater than a given positive number is located at half the asymptotic Gilbert-Varshamov bound.