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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 manifolds over and . Asymptotic expressions are obtained for the geodesic metric and projection Frobenius (chordal) metric on the manifold.

- 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 de ned as (p; q) = (sin2 1+ +sin2 k)1=2, where i; 1 i k, are the principal angles between p and q.

- 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
- Probl. Inf. Transm.
- 2006

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 finitedimensional operators related to orthogonal polynomials. The examples of the method considered in the paper include binary codes, binary constant-weight codes,… (More)

- 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)

- Dmitry Yu. Nogin
- Probl. Inf. Transm.
- 2005

We prove that the weight function wt: Fq → Z on a set of messages uniquely determines a linear code of dimension k up to equivalence. We propose a natural way to extend the rth generalized Hamming weight, that is, a function on r-subspaces of a code C, to a function on F( k r) q ∼= ΛC. Using this, we show that, for each linear code C and any integer r ≤ k =… (More)

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

Manuscript received December 18, 2004. A. Barg is with the Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742 USA (e-mail: abarg@umd.edu) D. Yu. Nogin is with the IPPI RAN, Bol’shoj Karetnyj 19, Moscow 101447, Russia (e-mail nogin@iitp.ru). Communicated by C. Carlet, Associate Editor for Coding Theory. Digital… (More)

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