New binary [72,36,12] self-dual codes from block circulant matrix
Cong Yu, Shixin Zhu, Tingting Wu · Research Square · 2023
Abstract In this work, we use five different forms of generator matrix to construct self-dual codes over $\mathbb{F}_{8}$. Then we establish a mapping from $\mathbb{F}_{8}$ to $\mathbb{F}_2$} which enables us to map a linear code of length $n$ over $\mathbb{F}_{8}$ to a binary linear code of length $3n$ and preserves orthogonality. We employ the five forms of generator matrix to construct binary [72,36,12] self-dual codes and find 180 singly-even and 1 doubly-even codes with new parameter in their weight enumerators which are not known before. We summarize all of our discoveries in tables.