Construction of some unimodular lattices with long shadow
Masaaki Harada
TL;DR
This paper constructs specific odd unimodular lattices in dimensions 36, 37, 41, 43, and 44 with particular minimum norms and shadow properties, expanding the catalog of such lattices.
Contribution
It introduces new constructions of odd unimodular lattices with prescribed minimum norms and shadow parameters in multiple dimensions.
Findings
Constructed odd unimodular lattices in dimensions 36, 37, 41, 43, 44.
Lattices have minimum norm 3 or 4 with specified shadow norms.
Extended the known examples of unimodular lattices with long shadows.
Abstract
In this paper, we construct odd unimodular lattices in dimensions n=36,37 having minimum norm 3 and 4s=n-16, where s is the minimum norm of the shadow. We also construct odd unimodular lattices in dimensions n=41,43,44 having minimum norm 4 and 4s=n-24.
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Taxonomy
TopicsCoding theory and cryptography · Algebraic structures and combinatorial models · Advanced Topics in Algebra