On the weight distribution of random binary linear codes

Nati Linial, Jonathan Mosheiff

Research output: Contribution to journalArticlepeer-review

8 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 languageEnglish
Pages (from-to)5-36
Number of pages32
JournalRandom Structures and Algorithms
Volume56
Issue number1
DOIs
StatePublished - 1 Jan 2020
Externally publishedYes

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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