Reversible Self-Dual Codes Over the Ring F2 + u F2
IEEE Access(2024)
摘要
In this study, we introduce bisymmetric self-dual codes over the finite field
${\mathbb F}_{2}$
of order two. We developed a method to generate binary bisymmetric self-dual codes from a small-length bisymmetric self-dual code by increasing its length. Using this method, we produced binary bisymmetric self-dual codes and discovered that numerous such codes exhibit favorable parameters. Also, we defined the map from binary bisymmetric self-dual codes to reversible self-dual codes over the ring
${\mathbb F}_{2}+u {\mathbb F}_{2}$
. This implies that there exists a one-to-one correspondence between the bisymmetric code over
${\mathbb F}_{2}$
and the reversible self-dual code over
${\mathbb F}_{2}+u {\mathbb F}_{2}$
. Consequently, using this map on generated bisymmetric self-dual codes, we obtained reversible self-dual codes over
${\mathbb F}_{2}+u {\mathbb F}_{2}$
, which were difficult to obtain using previously known methods.
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关键词
Code over a ring,reversible self-dual code,eigenvectors,bisymmetric matrix,bisymmetric self-dual codes
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