On the weight distribution of random binary linear codes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866917716708818944 |
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| author | Linial, Nati Mosheiff, Jonathan |
| author_facet | Linial, Nati Mosheiff, Jonathan |
| contents | We investigate the weight distribution of random binary linear codes. For $0<λ<1$ and $n\to\infty$ pick uniformly at random $λn$ vectors in $\mathbb{F}_2^n$ and let $C \le \mathbb{F}_2^n$ 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 $γn$. In this paper we determine the asymptotics of the moments of $X$ of all orders $o(\frac{n}{\log n})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1806_08392 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On the weight distribution of random binary linear codes Linial, Nati Mosheiff, Jonathan Information Theory Combinatorics We investigate the weight distribution of random binary linear codes. For $0<λ<1$ and $n\to\infty$ pick uniformly at random $λn$ vectors in $\mathbb{F}_2^n$ and let $C \le \mathbb{F}_2^n$ 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 $γn$. In this paper we determine the asymptotics of the moments of $X$ of all orders $o(\frac{n}{\log n})$. |
| title | On the weight distribution of random binary linear codes |
| topic | Information Theory Combinatorics |
| url | https://arxiv.org/abs/1806.08392 |