On the weight distribution of random binary linear codes

Nati Linial, Jonathan Mosheiff*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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 languageAmerican English
Pages (from-to)5-36
Number of pages32
JournalRandom Structures and Algorithms
Issue number1
StatePublished - 1 Jan 2020

Bibliographical note

Funding Information:
information: This research was supported by the ERC, 339096. Adams Fellowship Program of the Israel Academy of Sciences and Humanities.

Publisher Copyright:
© 2019 Wiley Periodicals, Inc.


  • exponential family
  • random linear code
  • weight distribution


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