Reversible Self-Dual Codes Over the Ring F2 + uF2
Hyun Jin Kim, Whan-Hyuk Choi · IEEE Access · 2023
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.