On the weight distribution of random binary linear codes
Nati Linial, Jonathan Mosheiff · Random Structures and Algorithms · 2019
We investigate the weight distribution of random binary linear codes. For 0 < λ < 1 and n→∞ pick uniformly at random λn vectors in and let 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 .