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

2017/09/11 by Chinen, Koji
#11T71 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1709.03403

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.

Related

• Construction of divisible formal weight enumerators and extremal polynomials not satisfying the Riemann hypothesis
• Zeta functions for formal weight enumerators and an analogue of the Mallows-Sloane bound
• On some families of divisible formal weight enumerators and their zeta functions
• Results on zeta functions for codes
• Weight enumerators, intersection enumerators and Jacobi polynomials II