On the image of code polynomials under theta map

The theta map sends code polynomials into the ring of Siegel modular forms of even weights. Explicit description of the image is known for $g\leq 3$ and the surjectivity of the theta map follows. Instead it is known that this map is not surjective for $g\geq 5$. In this paper we discuss the possibility of an embedding between the associated projective varieties. We prove that this is not possible for $g\geq 4$ and consequently we get the non surjectivity of the graded rings for the remaining case $g=4$

On the integral ring spanned by genus two weight enumerators

It is known that the weight enumerator of a self-dual doubly-even code in genus g = 1 can be uniquely written as an isobaric polynomial in certain homogeneous polynomials with integral coeffcients. We settle the case where g = 2 and prove the non-existence of such polynomials under some conditions

Remark on the weight enumerators and Siegel modular forms

The purpose of this note is to study the coefficients of the polynomials if we express the weight enumerator as the polynomial the fixed generators

On THE AVERAGE JOINT CYCLE INDEX AND THE AVERAGE JOINT WEIGHT ENUMERATOR (Research on finite groups, algebraic combinatorics, and vertex algebras)

In this paper, we introduce the concept of the complete joint cycle index and the average complete joint cycle index, and discuss a relation with the complete joint weight enumerator and the average complete joint weight enumerator respectively in coding theory

On the cycle index and the weight enumerator II

In the previous paper, the second and third named author introduced the concept of the complete cycle index and discussed a relation with the complete weight enumerator in coding theory. In the present paper, we introduce the concept of the complete joint cycle index and the average complete joint cycle index, and discuss a relation with the complete joint weight enumerator and the average complete joint weight enumerator respectively in coding theory. Moreover, the notion of the average intersection numbers is given, and we discuss a relation with the average intersection numbers in coding theory.Comment: 24 page