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June 2018 E-polynomials associated to $\mathbf{Z}_4$-codes
Togo MOTOMURA, Manabu OURA
Hokkaido Math. J. 47(2): 339-350 (June 2018). DOI: 10.14492/hokmj/1529308822

Abstract

Coding theory is connected with number theory via the invariant theory of some specified finite groups and theta functions. Under this correspondence we are interested in constructing, from a combinatorial point of view, an analogous theory of Eisenstein series. For this, we previously gave a formulation of E-polynomials based on the theory of binary codes. In the present paper we follow this direction and supply a new class of E-polynomials. To be precise, we introduce the E-polynomials associated to the $\mathbf{Z}_4$-codes and determine both the ring and the field structures generated by them. In addition, we discuss the zeros of the modular forms obtained from E-polynomials under the theta map.

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Togo MOTOMURA. Manabu OURA. "E-polynomials associated to $\mathbf{Z}_4$-codes." Hokkaido Math. J. 47 (2) 339 - 350, June 2018. https://doi.org/10.14492/hokmj/1529308822

Information

Published: June 2018
First available in Project Euclid: 18 June 2018

zbMATH: 06901709
MathSciNet: MR3815296
Digital Object Identifier: 10.14492/hokmj/1529308822

Subjects:
Primary: 11T71
Secondary: 11F46

Rights: Copyright © 2018 Hokkaido University, Department of Mathematics

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Vol.47 • No. 2 • June 2018
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