Search Results - "Avgustinovich, S. V."

Combinatorial Designs, Difference Sets, and Bent Functions as Perfect Colorings of Graphs and Multigraphs by Potapov, V. N., Avgustinovich, S. V.

“…We prove that (1): the characteristic function of each independent set in each regular graph attaining the Delsarte–Hoffman bound is a perfect coloring; (2):…”
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On Perfect Colorings of Paths Divisible by a Matching by Lisitsyna, M. A., Avgustinovich, S. V.

“…A vertex coloring of a graph is said to be perfect if the color structure of the neighborhood of each vertex depends only on the color of the vertex. We give a…”
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Maximum Intersection of Linear Codes and Codes Equivalent to Linear by Avgustinovich, S. V., Gorkunov, E. V.

“…We consider linear codes in a space over a finite field with the Hamming metric. A code is called pseudolinear if it is the image of a linear code under an…”
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Infinite permutations of lowest maximal pattern complexity by Avgustinovich, S.V., Frid, A., Kamae, T., Salimov, P.

“…An infinite permutation α is a linear ordering of N . We study properties of infinite permutations analogous to those of infinite words, and show some…”
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Multidimensional permanents in enumeration problems by Avgustinovich, S. V.

“…Permanents are an effective tool for solving many combinatorial problems about enumeration. The respective theory is well developed and has numerous…”
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Combinatorial designs, difference sets and bent functions as perfect colorings of graphs and multigraphs by Potapov, V. N, Avgustinovich, S. V

“…Siberian Mathematical Journal, 2020, Vol. 61, No. 5, P. 867-877 It is proved that 1) the indicator function of some onefold or multifold independent set in a…”
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Perfect 2-colorings of transitive cubic graphs by Avgustinovich, S. V., Lisitsyna, M. A.

“…For all transitive cubic graphs with atmost 18 vertices, we obtain a complete description for the admissible parameters of perfect 2-colorings…”
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On a code reconstruction by correlation coefficients of its subcodes by Avgustinovich, S. V., Gorkunov, E. V.

“…A generalization is obtained of the theorem on reconstruction of a binary code from dimensions of its subcodes. The notion is proposed of a correlation…”
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Perfect colorings of the Johnson graphs J(8, 3) and J(8, 4) with two colors by Avgustinovich, S. V., Mogil’nykh, I. Yu

“…In this article the parameter matrices are enumerated of all perfect 2-colorings of the Johnson graphs J (8, 3) and J (8, 4), and several constructions are…”
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On the reconstruction of binary codes from the dimensions of their subcodes by Gorkunov, E. V., Avgustinovich, S. V.

“…We prove that to reconstruct an arbitrary binary code up to equivalence it suffices to know the dimensions of all subcodes of even cardinality. It is shown…”
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Computation complexity of a ternary linear function by Avgustinovich, S. V., Vasil’ev, Yu. L., Rychkov, K. L.

“…The computation complexity is shown to equal 18 in the class of generalized (ternary) π -schemes of a ternary counter of order 3 that depend on tree variables…”
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Distance regular colorings of an infinite rectangular grid by Avgustinovich, S. V., Vasil’eva, A. Yu, Sergeeva, I. V.

“…The parameters are listed of all distance regular colorings of the infinite rectangular grid…”
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On perfect colorings of infinite multipath graphs by Lisitsyna, M. A, Avgustinovich, S. V, Parshina, O. G

“…Siberian Electronic Mathematical Reports 17 (2020) pp. 1863-1868 A coloring of vertices of a given graph is called perfect if the color structure of each ball…”
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On shifting sets in the binary hypercube by Vasil’ev, Yu. L., Avgustinovich, S. V., Krotov, D. S.

“…If two codes with distance 3 have some coincident neighborhoods then each of them is called a shifting set . In the binary (4 k + 3)-dimensional hypercube,…”
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The Classification of Some Perfect Codes by Avgustinovich, Sergey V., Heden, Olof, Solov’eva, Faina I.

“…Perfect 1-error correcting codes C in Z(2)(n), where n = 2(m) - 1, are considered. Let [C] denote the linear span of the words of C and let the rank of C be…”
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Perfect binary ( n,3) codes: the structure of graphs of minimum distances by Avgustinovich, S.V.

“…We prove that the graphs of minimum distances of two perfect binary ( n,3) codes are isomorphic if and only if these codes are equivalent…”
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On Intersection Problem for Perfect Binary Codes by Avgustinovich, Sergey V., Heden, Olof, Solov’eva, Faina I.

“…The main result is that to any even integer q in the interval 0 <= q <= 2(n+1-2) (log(n+1)), there are two perfect codes C-1 and C-2 of length n = 2(m) -1, m…”
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Minimal complexity of equidistributed infinite permutations by Avgustinovich, S.V., Frid, A.E., Puzynina, S.

“…An infinite permutation is a linear ordering of the set of natural numbers. An infinite permutation can be defined by a sequence of real numbers where only the…”
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Intersection matrices for partitions by binary perfect codes by Avgustinovich, S.V., Lobstein, A.C., Solov'eva, F.I.

“…We investigate the following problem: given two partitions of the Hamming space, their intersection matrix provides the cardinalities of the pairwise…”
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On the Number of -Perfect Binary Codes: A Lower Bound by Krotov, D S, Avgustinovich, S V

“…We present a construction of 1-perfect binary codes, which gives a new lower bound on the number of such codes. We conjecture that this lower bound is…”
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