Abstract
It is known that if C is an [24m + 2l, 12m + l, d] selfdual binary linear code with <TEX>$0{\leq}l<11,\;then\;d{\leq}4m+4$</TEX>. We present a sufficient condition for the nonexistence of extremal selfdual 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.
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