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arXiv · 1212.5679

Cumulative Distance Enumerators of Random Codes and their Thresholds

Yun Fan·San Ling·Hongwei Liu·Jing Shen·Chaoping Xing
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Abstract

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.

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Yun Fan, San Ling, Hongwei Liu, Jing Shen, Chaoping Xing. 2012-12-22. Cumulative Distance Enumerators of Random Codes and their Thresholds. https://arxiv.org/abs/1212.5679

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