Abstract: We consider a construction of additive codes with parameters $[p^2+2,2.5,p^2]_{p^2}$ (codes over GF$(p^2)$ of length $p^2+2$, GF$(p)$-dimension $5$, and distance $p^2$) with a prescribed automorphism group of order $p^2$ generated by the matrices $\left(\begin{smallmatrix} 1 & 0 & 1 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \end{smallmatrix}\right)$, $\left(\begin{smallmatrix} 1 & 0 & 0 & a & 0 \\ 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 & 1 \end{smallmatrix}\right)$. Alternatively, the construction can be treated as a partial extension of an oval in a projective plain. This is joint work with Sascha Kurz.

Cite: Krotov D.
Additive codes by extending ovals
The 31st AHJZU-AHU-USTC Joint International Seminar on Algebraic Combinatorics 28-30 Nov 2025