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.).
Bibliographical noteFunding Information:
information: This research was supported by the ERC, 339096. Adams Fellowship Program of the Israel Academy of Sciences and Humanities.
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- exponential family
- random linear code
- weight distribution