On the weight distribution of random binary linear codes

Nati Linial; Jonathan Mosheiff

doi:10.1002/rsa.20879

On the weight distribution of random binary linear codes

Nati Linial, Jonathan Mosheiff

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

We investigate the weight distribution of random binary linear codes. For 0 < λ < 1 and n→∞ pick uniformly at random λn vectors in (Formula presented.) and let (Formula presented.) 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 (Formula presented.).

Original language	English
Pages (from-to)	5-36
Number of pages	32
Journal	Random Structures and Algorithms
Volume	56
Issue number	1
DOIs	https://doi.org/10.1002/rsa.20879
State	Published - 1 Jan 2020
Externally published	Yes

Keywords

exponential family
random linear code
weight distribution

ASJC Scopus subject areas

Software
General Mathematics
Computer Graphics and Computer-Aided Design
Applied Mathematics

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10.1002/rsa.20879

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KW - weight distribution

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On the weight distribution of random binary linear codes

Abstract

Keywords

ASJC Scopus subject areas

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