Mathematical Journal of Okayama University volume63 issue1
2021-01 発行

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

Chinen, Koji Department of Mathematics, School of Science and Engineering, Kindai University
Publication Date
2021-01
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.
Keywords
Binomial moment
Divisible code
Invariant polynomial ring
Zeta function for codes
Riemann hypothesis
Comments
Mathematics Subject Classification. Primary 11T71; Secondary 13A50, 12D10.