Dmitry Yu. Nogin

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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)
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)
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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