Mathematics – Combinatorics
Scientific paper
2010-06-11
Mathematics
Combinatorics
16 pages. minor revision
Scientific paper
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 from 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.
Munemasa Akihiro
Tamura Hiroki
No associations
LandOfFree
The codes and the lattices of Hadamard matrices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The codes and the lattices of Hadamard matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The codes and the lattices of Hadamard matrices will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-644783