# IJPAM: Volume 29, No. 3 (2006)

**TERNARY CODES AND THETA-FUNCTIONS**

Department of Mathematics and Computing Science

Eindhoven University of Technology

P.O. Box 513, MB Eindhoven, 5600, THE NETHERLANDS

e-mail: a.g.v.asch@tue.nl

**Abstract.**There is a remarkable connection between the theory of modular forms, in particular theta functions, and coding theory, the connection being established by defining a suitable lattice corresponding to the given code. First we determine some transformation formulas for certain theta functions. Then it is proved that the theta function of the lattice corresponding to the code can be expressed in terms of the Hamming weight enumerator. In particular if the code is self-dual and the length is a multiple of this theta function is a modular form for some subgroup of the modular group. And using the structure of this space of modular forms we can describe the weight distribution of the code.

**Received: **May 12, 2006

**AMS Subject Classification: **11F11, 11F27, 94B05

**Key Words and Phrases: **modular form, theta function, ternary code, weight enumerator

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2006

**Volume:** 29

**Issue:** 3