On the number of error correcting codes
نویسندگان
چکیده
Abstract We show that for a fixed $q$ , the number of -ary $t$ -error correcting codes length $n$ is at most $2^{(1 + o(1)) H_q(n,t)}$ all $t \leq (1 - q^{-1})n 2\sqrt{n \log n}$ where $H_q(n, t) = q^n/ V_q(n,t)$ Hamming bound and $V_q(n,t)$ cardinality radius ball. This proves conjecture Balogh, Treglown, Wagner, who showed result o(n^{1/3} (\log n)^{-2/3})$ .
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ژورنال
عنوان ژورنال: Combinatorics, Probability & Computing
سال: 2023
ISSN: ['0963-5483', '1469-2163']
DOI: https://doi.org/10.1017/s0963548323000111