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• W2017690252 abstract "We develop a construction method for finding self-dual codes with an automorphism of order $p$ with $c$ independent $p$-cycles. In more detail, we construct a self-dual code with an automorphism of type $p-(c,f+2)$ and length $n+2$ from a self-dual code with an automorphism of type $p-(c,f)$ and length $n$, where an <em>automorphism of type</em> $p-(c, f)$ is that of order $p$ with $c$ independent cycles and $f$ fixed points. Using this construction, we find three new inequivalent extremal self-dual $[54, 27, 10]$ codes with an automorphism of type $7-(7,5)$ and two new inequivalent extremal self-dual $[58, 29, 10]$ codes with an automorphism of of type $7-(8,2)$. We also obtain an extremal self-dual $[40, 20, 8]$ code with an automorphism of type $3-(10, 10)$, which is constructed from an extremal self-dual $[38, 19, 8]$ code of type $3-(10,8)$, and at least 482 inequivalent extremal self-dual $[58,29,10]$ codes with an automorphism of type $3-(18,4)$, which is constructed from an extremal self-dual $[54, 27, 10]$ code of type $3-(18,0);$ we note that the extremality is preserved." @default.
• W2017690252 created "2016-06-24" @default.
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• W2017690252 date "2011-01-01" @default.
• W2017690252 modified "2023-10-16" @default.
• W2017690252 title "Construction of self-dual codes with an automorphism of order $p$" @default.
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• W2017690252 doi "https://doi.org/10.3934/amc.2011.5.23" @default.
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