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On the weight distribution of random binary linear codes

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 04 Jul 2019Embargo end date: 01 Jan 2018 English Publisher:WileyJournal:Random Structures & Algorithms, volume 56, pages 5-36 (issn: 1042-9832, eissn: 1098-2418, Copyright policy )
Authors: Nati Linial; Jonathan Mosheiff;

doi: 10.1002/rsa.20879 , 10.48550/arxiv.1806.08392

arXiv: 1806.08392

On the weight distribution of random binary linear codes

Abstract

We investigate the weight distribution of random binary linear codes. For 0 < λ < 1 and n→∞ pick uniformly at random λn vectors in and let be the orthogonal complement of their span. Given 0 < γ < 1/2 with 0 < λ < h(γ) let X be the random variable that counts the number of words in C of Hamming weight γn. In this paper we determine the asymptotics of the moments of X of all orders .

Related Organizations
Keywords

FOS: Computer and information sciences, Combinatorial probability, Computer Science - Information Theory, Information Theory (cs.IT), weight distribution, Bounds on codes, exponential family, FOS: Mathematics, Mathematics - Combinatorics, Probability distributions: general theory, Combinatorics (math.CO), random linear code, Linear codes (general theory)

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    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
9
Top 10%
Top 10%
Top 10%
Green
bronze