Weight distribution of random linear codes and Krawtchouk polynomials

Alex Samorodnitsky

Research output: Contribution to journalArticlepeer-review


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

Original languageEnglish
JournalRandom Structures and Algorithms
StateAccepted/In press - 2024
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2024 The Authors. Random Structures & Algorithms published by Wiley Periodicals LLC.


  • Krawtchouk polynomials
  • random linear codes
  • weight distribution


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