Abstract
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 language | English |
|---|---|
| Pages (from-to) | 261-274 |
| Number of pages | 14 |
| Journal | Random Structures and Algorithms |
| Volume | 65 |
| Issue number | 2 |
| DOIs | |
| State | Published - Sep 2024 |
Bibliographical note
Publisher Copyright:© 2024 The Authors. Random Structures & Algorithms published by Wiley Periodicals LLC.
Keywords
- Krawtchouk polynomials
- random linear codes
- weight distribution