Designs and their codes
Construction of new extremal unimodular lattices
European Journal of Combinatorics - Special issue on arithmétique et combinatoire
On some self-dual codes and unimodular lattices in dimension 48
European Journal of Combinatorics
IEEE Transactions on Information Theory
On ternary self-dual codes of length 24
IEEE Transactions on Information Theory
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It has been observed by Assmus and Key as a result of the complete classification of Hadamard matrices of order 24, that the extremality of the binary code of a Hadamard matrix H of order 24 is equivalent to the extremality of the ternary code of H^T. In this note, we present two proofs of this fact, neither of which depends on the classification. One is a consequence of a more general result on the minimum weight of the dual of the code of a Hadamard matrix. The other relates the lattices obtained from the binary code and the ternary code. Both proofs are presented in greater generality to include higher orders. In particular, the latter method is also used to show the equivalence of (i) the extremality of the ternary code, (ii) the extremality of the Z"4-code, and (iii) the extremality of a lattice obtained from a Hadamard matrix of order 48.