Mathematical Journal of Okayama University volume63 issue1
Department of Mathematics, School of Science and Engineering, Kindai University
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.
Invariant polynomial ring
Zeta function for codes
Mathematics Subject Classiﬁcation. Primary 11T71; Secondary 13A50, 12D10.