Mass formula for various generalized weight enumerators of binary self-dual codes
نویسندگان
چکیده
In this paper we give extensions of the mass formula for biweight enumerators and the Jacobi weight enumerators of binary self-dual codes and binary doubly even self-dual codes. For binary doubly even self-dual codes, our formula is expressed in terms of the root system E8 embedded in C4 for biweight enumerators, while the root system D4 is employed for Jacobi weight enumerators. For self-dual codes, the mass formula for biweight enumerators (resp. Jacobi weight enumerators) is controlled by the root system F4 (resp. B2). We show that, in some cases, the mass formula is already sufficient to generate the ring of invariants of a certain finite group. The mass formula for Jacobi weight enumerators can be used to construct Jacobi forms, and we give an explicit example which differ from the Eisenstein– Jacobi series.
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