Maya Stoyanova

New nonexistence results for spherical designs

New nonexistence results for spherical designs of odd strength and odd cardinality are proved by improvements on previously applied polynomial techniques. This implies new bounds on the designs under consideration either in small dimensions and in certain asymptotic process.

Energy bounds for codes and designs in Hamming spaces

We obtain universal bounds on the energy of codes and designs in Hamming spaces. Our bounds hold for a large class of potential functions, allow a unified treatment, and can be viewed as a generalization of the Levenshtein bounds for maximal codes.

Nonexistence of binary orthogonal arrays via their distance distributions

We investigate binary orthogonal arrays by making use of the fact that all possible distance distributions of the arrays under investigation and of related arrays can be computed. We apply certain relations for reducing the number of feasible distance distributions. In some cases this leads to nonexistence results. In particular, we prove that there exist no binary orthogonal arrays with parameters (strength, length, cardinality) = (4, 10, 6 · 24), (4, 11, 6 · 24), (4, 12, 7 · 24), (5, 11, 6 · 25), (5, 12, 6 · 25), and (5, 13, 7 · 25).

A method for proving nonexistence of spherical designs of odd strength and odd cardinality

We combine polynomial techniques with some geometric arguments to obtain restrictions of the structure of spherical designs with fixed odd strength and odd cardinality. Our bounds for the extreme inner products of such designs allow us to prove nonexistence results in many cases. Applications are shown for 7-designs.

Nonexistence of a few binary orthogonal arrays

We develop and apply combinatorial algorithms for investigation of the feasible distance distributions of binary orthogonal arrays with respect to a point of the ambient binary Hamming space utilizing constraints imposed from the relations between the distance distributions of connected arrays. This turns out to be strong enough and we prove the nonexistence of binary orthogonal arrays of parameters (length, cardinality, strength)

A new asymptotic bound of the minimum possible odd cardinality of spherical (2k-1 )-designs

\ =(9,6.2^4=96,4)

On spherical codes with inner products in a prescribed interval

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Nonexistence of (9, 112, 4) and (10, 224, 5) binary orthogonal arrays

(10,6.2^5,5)

Universal Lower Bounds on Energy and LP-Extremal Polynomials for (4, 24)-Codes

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Lower energy bounds for antipodal spherical codes and for codes in infinite projective spaces

(10,7.2^4=112,4)