arXiv subjects

Dmitry Nogin

Publications and source records attributed to Dmitry Nogin.

3 recordsLinked to original sources

arXiv2008

A functional view of upper bounds on codes

Functional and linear-algebraic approaches to the Delsarte problem of upper bounds on codes are discussed. We show that Christoffel-Darboux kernels and Levenshtein polynomials related to them arise as stationary points of the moment functionals of some distributions. We also show that they can be derived as eigenfunctions of the Jacobi operator. This motivates the choice of polynomials used to derive linear programming upper bounds on codes in homogeneous spaces.

cs.IT↗

arXiv2006

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.

cs.IT↗

arXiv2005

A bound on Grassmannian codes

We give a new asymptotic upper bound on the size of a code in the Grassmannian space. The bound is better than the upper bounds known previously in the entire range of distances except very large values.

cs.IT↗