On some families of invariant polynomials divisible by three and their zeta functions

Koji Chinen

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arXiv · 1709.03403

On some families of invariant polynomials divisible by three and their zeta functions

Koji Chinen

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Abstract

In this note, we establish an analog of the Mallows-Sloane bound for Type III formal weight enumerators. This completes the bounds for all types (Types I through IV) in synthesis of our previous results. Next we show by using the binomial moments that there exists a family of polynomials divisible by three, which are not related to linear codes but are invariant under the MacWilliams transform for the value 3/2. We also discuss some properties of the zeta functions for such polynomials.

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Koji Chinen. 2017-09-11. On some families of invariant polynomials divisible by three and their zeta functions. https://arxiv.org/abs/1709.03403

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