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作者机构:Hebrew Univ Jerusalem Dept Comp Sci IL-9190401 Jerusalem Israel
出 版 物:《RANDOM STRUCTURES & ALGORITHMS》 (随机结构和算法)
年 卷 期:2020年第56卷第1期
页 面:5-36页
核心收录:
学科分类:07[理学] 0835[工学-软件工程] 0701[理学-数学] 070101[理学-基础数学]
基 金:ERC Adams Fellowship Program of the Israel Academy of Sciences and Humanities European Research Council (ERC) Funding Source: European Research Council (ERC)
主 题:exponential family random linear code weight distribution
摘 要:We investigate the weight distribution of random binary linear codes. For 0 infinity pick uniformly at random lambda n vectors in F2n and let C = F2n be the orthogonal complement of their span. Given 0 gamma 1/2 with 0 lambda h(gamma) let X be the random variable that counts the number of words in C of Hamming weight gamma n. In this paper we determine the asymptotics of the moments of X of all orders o(nlogn).