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We prove that the automorphism group of a putative binary self-dual doubly-even [72,36,16] code is solvable. Moreover, its order is 5, 7, 10, 14, 56, or a divisor of 72.
In this paper, extremal singly even self-dual codes with minimal shadow are investigated. Nonexistence of such codes for particular parameters is proved. By a result of Rains, the length of extremal singly even self-dual codes is bounded. Explicit bounds are given in case the shadow is minimal.
— We prove that the automor-phism group of a binary self-dual doubly-even [72, 36, 16] code has order 5, 7, 10, 14 or d where d divides 18 or 24, or it is A4 × C3.
Using representation theoretical methods we investigate self-dual group codes and their extensions in characteristic 2. We prove that the existence of a self-dual extended group code heavily depends on a particular structure of the group algebra KG which can be checked by an easy-to-handle criteria in elementary number theory. Surprisingly, in the binary… (More)
Let <i>C</i> be a binary extremal self-dual code of length <i>n</i> ¿ 48. We prove that for each <i>¿ ¿ Aut(C</i>) of prime order <i>p</i> ¿ 5 the number of fixed points in the permutation action on the coordinate positions is bounded by the number of <i>p</i>-cycles. It turns out that large primes <i>p</i>, i.e., <i>n</i>-<i>p</i> small, seem to occur in… (More)