Eisenstein lattices, Galois rings, and theta series

Authors:
Kok Seng Chua;Patrick Solé
Affiliations:
Department of Mathematics, National University of Singapore, Singapore 117543, Republic of Singapore;CNRS-I3S, ESS1, Route des Colles, 06 903 Sophia Antipolis, France
Venue:
European Journal of Combinatorics - Special issue on algebraic combinatorics: in memory of J.J. Seidel
Year:
2004

Citing 3
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Abstract

The Shrikhande graph is classically described in terms of a Galois ring of order 16 viewed as the Eisenstein integers modulo 4. Codes over that ring (but for a different weight) give rise to Eisenstein lattices, the theta series of which is expressed as a polynomial into three special theta series. As a special case the theta series of a lattice obtained by the complex Construction B from quaternary codes is derived.