Uniqueness of certain completely regular Hadamard codes

Details Uniqueness of certain completely regular Hadamard codes Uniqueness of certain completely regular Hadamard codes

2011-12-06

arxiv.org/abs/1112.1247v2

Mathematics

Combinatorics

Scientific paper

We classify binary completely regular codes of length $m$ with minimum distance $\delta$ for $(m,\delta)=(12,6)$ and $(11,5)$. We prove that such codes are unique up to equivalence, and in particular, are equivalent to certain Hadamard codes. We prove that the automorphism groups of these Hadamard codes, modulo the kernel of a particular action, are isomorphic to certain Mathieu groups, from which we prove that completely regular codes with these parameters are necessarily completely transitive.

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