On a 5-design related to a putative extremal doubly even self-dual code of length a multiple of 24

Abstract

By the Assmus and Mattson theorem, the codewords of each nontrivial weight in an extremal doubly even self-dual code of length 24m form a self-orthogonal 5-design. In this paper, we study the codes constructed from self-orthogonal 5-designs with the same parameters as the above 5-designs. We give some parameters of a self-orthogonal 5-design whose existence is equivalent to that of an extremal doubly even self-dual code of length 24m for m=3,...,6. If $m\in \{1,\dots ,6\}$, $k\in \{m+1,\dots ,5m-1\}$ and $(m,k)\ne (6,18)$, then it is shown that an extremal doubly even self-dual code of length 24m is generated by codewords of weight 4k.

16 pages, Designs, Codes and Cryptogr. (to appear)