Journal of the
Korean Mathematical Society JKMS

It is known that if $C$ is an $[24m+2l, 12m+l,d~]$ self-dual binary linear code with $0 \leq l < 11$, then $d \leq 4m+4$. We present a sufficient condition for the nonexistence of extremal self-dual binary linear codes with $d=4m+4, l=1,2,3,5$. From the sufficient condition, we calculate $m$'s which correspond to the nonexistence of some extremal self-dual binary linear codes. In particular, we prove that there are infinitely many such $m$'s. We also give similar results for additive self-dual codes over $GF(4)$ of length $n=6m+1$.

Keywords: self-dual code, extremal code, shadow

MSC numbers: Primary 94B60, 94B65