Reversible Self-Dual Codes Over the Ring F2 + uF2

초록

In this study, we introduce bisymmetric self-dual codes over the finite field 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 F-2 + uF(2). This implies that there exists a one-to-one correspondence between the bisymmetric code over F-2 and the reversible self-dual code over F-2 + uF(2) . Consequently, using this map on generated bisymmetric self-dual codes, we obtained reversible self-dual codes over F-2 + uF(2), which were difficult to obtain using previously known methods.

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