12,180 research outputs found
Spectral approach to linear programming bounds on codes
We give new proofs of asymptotic upper bounds of coding theory obtained
within the frame of Delsarte's linear programming method. The proofs rely on
the analysis of eigenvectors of some finite-dimensional operators related to
orthogonal polynomials. The examples of the method considered in the paper
include binary codes, binary constant-weight codes, spherical codes, and codes
in the projective spaces.Comment: 11 pages, submitte
Lecture notes: Semidefinite programs and harmonic analysis
Lecture notes for the tutorial at the workshop HPOPT 2008 - 10th
International Workshop on High Performance Optimization Techniques (Algebraic
Structure in Semidefinite Programming), June 11th to 13th, 2008, Tilburg
University, The Netherlands.Comment: 31 page
Linear programming bounds for doubly-even self-dual codes
Using a variant of linear programming method we
derive a new upper bound on the minimum distance d of doubly-even self-dual codes of length n. Asymptotically, for n growing, it gives d/n <=166315 + o(1), thus improving on the Mallows–
Odlyzko–Sloane bound of 1/6. To establish this, we prove that in any doubly even-self-dual code the distance distribution is asymptotically upper-bounded by the corresponding normalized binomial distribution in a certain interval
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