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 | |
| State | Published - 1 Jan 2020 |
Bibliographical note
Publisher Copyright:© 2019 Wiley Periodicals, Inc.
Keywords
- exponential family
- random linear code
- weight distribution