In this note we investigate extremal singly-even self-dual codes with minimal shadow. For particular parameters we prove non-existence of such codes. By a result of Rains , the length of extremal singly-even self-dual codes is bounded. We give explicit bounds in case the shadow is minimal. 1 Introduction Let C be a singly-even self-dual [n, n 2 , d] code… (More)
— 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.
Based on results in finite geometry we prove the existence of MRD codes in (F q) n,n with minimum distance n which are essentially different from Gabidulin codes. The construction results from algebraic structures which are closely related to those of finite fields. Furthermore we show that an analogue of MacWilliams' extension theorem does not exist for… (More)