| Generalized H-codes and Doubly Even Self Dual Binary Codes (2007) | |||||||||||||
Abstract | |||||||||||||
| A generalized H-code is defined by Bhattacharya as a special kind of Abelian codes. In this paper, we define GH-set and give some necessary and sufficient conditions for a generalized H-code to be doubly even self-dual. Some examples of such doubly even self-dual codes are also given. 1 Introduction It is well-known that cyclic codes may be seen as principal ideals in a semisimple algebra. A natural generalization of cyclic codes is the class of Abelian codes. Let G be an Abelian group, F a finite field, and FG the corresponding group algebra. A nonzero ideal of FG is called an Abelian code. Camion [2] introduced a special class of Abelian codes which is then referred to as H-code (see [8],[9]). An H-code is defined in FG, where F is a finite field of characteristic 2 and G is an elementry Abelian 2-group. This code is proved to be self-dual and that it is doubly even if and only if the weight of the generating element is a multiple of 4. Bhattacharya [1] defined a generalized H-code ... | |||||||||||||
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