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Random Structures and Algorithms
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Weight distribution of random linear codes and Krawtchouk polynomials

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 15 Mar 2024Embargo end date: 01 Jan 2022 English Publisher:WileyJournal:Random Structures & Algorithms, volume 65, pages 261-274 (issn: 1042-9832, eissn: 1098-2418, Copyright policy )
Authors: Alex Samorodnitsky;

doi: 10.1002/rsa.21214 , 10.48550/arxiv.2205.02051

arXiv: 2205.02051

Weight distribution of random linear codes and Krawtchouk polynomials

Abstract

AbstractFor and pick uniformly at random vectors in and let be the orthogonal complement of their span. Given with , let be the random variable that counts the number of words in of Hamming weight (where is assumed to be an even integer). Linial and Mosheiff [Random Struct. Algorithms. 62 (2023), 68Ű‐130] determined the asymptotics of the moments of of all orders . In this paper we extend their estimates up to moments of linear order. Our key observation is that the behavior of the suitably normalized moment of is essentially determined by the norm of the Krawtchouk polynomial .

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Keywords

FOS: Computer and information sciences, Combinatorial codes, Computer Science - Information Theory, Information Theory (cs.IT), random linear codes, weight distribution, FOS: Mathematics, Mathematics - Combinatorics, Krawtchouk polynomials, Combinatorics (math.CO), Linear codes (general theory)

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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!
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