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- Alexander Barg, Dmitry Yu. Nogin
- IEEE Trans. Information Theory
- 2002

—We derive the Gilbert–Varshamov and Hamming bounds for packings of spheres (codes) in the Grassmann mani-folds over and. Asymptotic expressions are obtained for the geodesic metric and projection Frobenius (chordal) metric on the manifold.

Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given.… (More)

- B. V. Karpov, D. Yu. Nogin
- 1998

We study complete exceptional collections of coherent sheaves over Del Pezzo surfaces, which consist of three blocks such that inside each block all Ext groups between the sheaves are zero. We show that the ranks of all sheaves in such a block are the same and the three ranks corresponding to a complete 3-block exceptional collection satisfy a Markov-type… (More)

We derive the Varshamov{Gilbert and Hamming bounds for packings of spheres (codes) in the Grassmann manifolds over R and C. The distance between two k-planes is deened as (p; q) = (sin 2 1 + +sin 2 k) 1=2 , where i ; 1 i k, are the principal angles between p and q.

- Alexander Barg, Dmitry Yu. Nogin
- Probl. Inf. Transm.
- 2006

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. the problem of estimating the number of planes whose pairwise distances are bounded below by some given value δ, for a suitably defined distance function… (More)

- Alexander Barg, Dmitry Yu. Nogin
- 2006 IEEE International Symposium on Information…
- 2006

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

- Alexander Barg, Dmitry Yu. Nogin
- ArXiv
- 2007

1. Introduction. In the problem of bounding the size of codes in compact homogeneous spaces, Del-sarte's polynomial method gives rise to the most powerful universal bounds on codes. Many overviews of the method exist in the literature; see for instance Levenshtein (1998). The purpose of this talk is to present a functional perspective of this method and… (More)

— We give a new proof of the asymptotic upper bound on the size of binary codes obtained within the frame of Delsarte's linear programming method. The proof relies on the analysis of eigenvectors of some finite-dimensional operators related to Krawtchouk polynomials.

- Alexander Barg, Dmitry Yu. Nogin
- IEEE Trans. Information Theory
- 2005