Codes over GF(4) and complex lattices

Abstract

This paper studies the relationship between error-correcting codes over GF(4) and complex lattices (more precisely, $\text{Z}$[ω]-modules in $\text{C}$ⁿ, where $\text{ω = e}{}^{\mathrm{<mtext>2\pi i</mtext><mtext>3</mtext>}}$). The theta-functions of self-dual lattices are characterized. Two general methods are presented for constructing lattices from codes. Several examples are given, including a new lattice sphere-packing in $\text{R}$³⁶.