Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
A new upper bound on nonbinary block codes
Discrete Mathematics - Coding Theory
The binary self-dual codes of length up to 32: a revised enumeration
Journal of Combinatorial Theory Series A
Algebraic-Geometric Codes
There is no (24, 12, 10) self-dual quaternary code
IEEE Transactions on Information Theory
New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities
IEEE Transactions on Information Theory
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In the present paper, we make use of the quadratic field Q(-3) to construct dense packings in the Euclidean spaces. With the help from good error-correcting codes, we are able to produce several packings with the best-known densities. Furthermore, if we assume that the best upper bound in coding theory developed by Aaltonen, Ben-Haim and Litsyn could be achieved, then the Minkowski bound would be improved.