On extended perfect codes
| Autor: | Vorob'ev, Konstantin |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We consider extended $1$-perfect codes in Hamming graphs $H(n,q)$. Such nontrivial codes are known only when $n=2^k$, $k\geq 1$, $q=2$, or $n=q+2$, $q=2^m$, $m\geq 1$. Recently, Bespalov proved nonexistence of extended $1$-perfect codes for $q=3$, $4$, $n>q+2$. In this work, we characterize all positive integers $n$, $r$ and prime $p$, for which there exist such a code in $H(n,p^r)$. Comment: 6 pages |
| Databáze: | arXiv |
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