15:{"metadata":[["$","title","0",{"children":"On the weight distribution of random binary linear codes"}],["$","meta","1",{"name":"description","content":"We investigate the weight distribution of random binary linear codes. For $0<\\lambda<1$ and $n\\to\\infty$ pick uniformly at random $\\lambda n$ vectors in $\\mathbb{F}_2^n$ and let $C \\le \\mathbb{F}_2^n$ 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 $o(\\frac{n}{\\log n})$."}],["$","meta","2",{"name":"author","content":"Nati Linial"}],["$","meta","3",{"name":"author","content":"Jonathan Mosheiff"}],["$","meta","4",{"name":"keywords","content":"Information Theory,Combinatorics"}],["$","meta","5",{"name":"referrer","content":"origin"}],["$","meta","6",{"name":"robots","content":"index, follow"}],["$","link","7",{"rel":"canonical","href":"https://synthical.com/article/On-the-weight-distribution-of-random-binary-linear-codes-6214dd02-ffba-11ed-9b54-72eb57fa10b3"}],["$","link","8",{"rel":"alternate","hrefLang":"de-DE","href":"https://synthical.com/article/On-the-weight-distribution-of-random-binary-linear-codes-6214dd02-ffba-11ed-9b54-72eb57fa10b3/de"}],["$","link","9",{"rel":"alternate","hrefLang":"fr-FR","href":"https://synthical.com/article/On-the-weight-distribution-of-random-binary-linear-codes-6214dd02-ffba-11ed-9b54-72eb57fa10b3/fr"}],["$","link","10",{"rel":"alternate","hrefLang":"es-ES","href":"https://synthical.com/article/On-the-weight-distribution-of-random-binary-linear-codes-6214dd02-ffba-11ed-9b54-72eb57fa10b3/es"}],["$","link","11",{"rel":"alternate","hrefLang":"it-IT","href":"https://synthical.com/article/On-the-weight-distribution-of-random-binary-linear-codes-6214dd02-ffba-11ed-9b54-72eb57fa10b3/it"}],["$","link","12",{"rel":"alternate","hrefLang":"ru-RU","href":"https://synthical.com/article/On-the-weight-distribution-of-random-binary-linear-codes-6214dd02-ffba-11ed-9b54-72eb57fa10b3/ru"}],["$","meta","13",{"property":"og:title","content":"On the weight distribution of random binary linear codes"}],["$","meta","14",{"property":"og:description","content":"We investigate the weight distribution of random binary linear codes. 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In this paper we determine the asymptotics of the moments of $X$ of all orders $o(\\frac{n}{\\log n})$."}],["$","meta","15",{"property":"og:url","content":"https://synthical.com/article/On-the-weight-distribution-of-random-binary-linear-codes-6214dd02-ffba-11ed-9b54-72eb57fa10b3"}],["$","meta","16",{"property":"og:site_name","content":"Synthical"}],["$","meta","17",{"property":"og:locale","content":"en-US"}],["$","meta","18",{"property":"og:image","content":"https://synthical.com/preview/article/6214dd02-ffba-11ed-9b54-72eb57fa10b3"}],["$","meta","19",{"property":"og:image:alt","content":"On the weight distribution of random binary linear codes"}],["$","meta","20",{"property":"og:image:width","content":"1200"}],["$","meta","21",{"property":"og:image:height","content":"630"}],["$","meta","22",{"property":"og:type","content":"article"}],["$","meta","23",{"property":"article:published_time","content":"2018-06-21T18:42:56.000Z"}],["$","meta","24",{"property":"article:modified_time","content":"2018-06-21T18:42:56.000Z"}],["$","meta","25",{"property":"article:author:name","content":"Nati Linial"}],["$","meta","26",{"property":"article:author:name","content":"Jonathan Mosheiff"}],["$","meta","27",{"property":"article:author:id","content":"7a3e0f68-f661-4793-9110-b3929dc9a1cb"}],["$","meta","28",{"property":"article:author:alternatives","content":"Jonathan Mosheiff,J. 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