Improved lower bounds for self-dual codes over $ \mathbb{F}_{11} $, $ \mathbb{F}_{13} $, $ \mathbb{F}_{17} $, $ \mathbb{F}_{19} $ and $ \mathbb{F}_{23} $
Thomas Aaron Gulliver, Masaaki Harada · Advances in Mathematics of Communications · 2022
We construct self-dual codes over \begin{document}$ \mathbb{F}_{11} $\end{document} , \begin{document}$ \mathbb{F}_{13} $\end{document} , \begin{document}$ \mathbb{F}_{17} $\end{document} , \begin{document}$ \mathbb{F}_{19} $\end{document} and \begin{document}$ \mathbb{F}_{23} $\end{document} which improve the previously known lower bounds on the largest minimum weights. In particular, the largest possible minimum weight among self-dual \begin{document}$ [n, n/2] $\end{document} codes over \begin{document}$ \mathbb{F}_{p} $\end{document} is determined for \begin{document}$ (p, n) = (19, 24) $\end{document} and \begin{document}$ (23, 28) $\end{document} .