On the weight distribution of random binary linear codes

06/21/2018

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by   Nati Linial, et al.

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We investigate the weight distribution of random binary linear codes. For 0<λ<1 and n→∞ pick uniformly at random λ n vectors in F_2^n and let C <F_2^n 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 γ n. In this paper we determine the asymptotics of the moments of X of all orders o(n/ n).