Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Double Circulant Codes over Z\!Z_{\bf 4}and Even Unimodular Lattices
Journal of Algebraic Combinatorics: An International Journal
An optimal unimodular lattice in dimension 39
Journal of Combinatorial Theory Series A
Ternary Code Construction of Unimodular Lattices and Self-Dual Codes over \Bbb Z6
Journal of Algebraic Combinatorics: An International Journal
Quadratic double circulant codes over fields
Journal of Combinatorial Theory Series A
A mass formula for unimodular lattices with no roots
Mathematics of Computation
Experimental constructions of self-dual codes
Finite Fields and Their Applications
The codes and the lattices of Hadamard matrices
European Journal of Combinatorics
On the classification and enumeration of self-dual codes
Finite Fields and Their Applications
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In this paper we construct new extremal and optimal unimodular lattices in dimensions 36, 38, 42, 45, 52, 54, 60 and 68. We construct them in two ways: first in the case of dimensions congruent to 4 modulo 8 by construction B3 followed by density doubling, generalizing the constructions of Sphere Packing Lattices and Groups (1988) 148 and Théorie des Nombres (1989) 772; and second by applying the well known Construction A to self-dual codes over GF(5) and to codes over the ring Z/25Z. In particular the lattice in dimension 60, P60q, generalizes the construction of the lattice P48q. We also give the complete weight enumerator of the extended ternary quadratic residue code of length 60 and we provide a table of the best known unimodular lattices of dimensions up to 80.