On the structure of some arcs related to caps and the nonexistence of some optimal codes (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 2019)
In this paper we solve two instances of the main problem in coding theory for linear codes of dimension 5 over $\mathbb{F}_4$. We prove the nonexistence of $[395,5,295]_4$- and $[396,5,296]_4$-codes which implies the exact values $n_4(5,295)=396$ and $n_4(5,296)=397$. As a by-product, we characterize the arcs with parameters $(100,26)$ in $PG(3,4)$.