Sobolev Institute of Mathematics

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19932026

most citedPhysics Interplay of the LHC and the ILC

408 citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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32 papers · 1 filter

cs.IT2023★ 1 cited

Multispreads

Denis S. Krotov, Ivan Yu. Mogilnykh

Additive one-weight codes over a finite field of non-prime order are equivalent to special subspace coverings of the points of a projective space, which we call multispreads. The c…

cs.IT2023★ 2 cited

Existence of balanced functions that are not derivative of bent functions

Vladimir N. Potapov

It is disproved the Tokareva's conjecture that any balanced boolean function of appropriate degree is a derivative of some bent function. This result is based on new upper bounds f…

cs.IT2022

Linear and group perfect codes over skew fields and quasi skew fields

Sergei A. Malyugin

In this paper, we propose a general construction of linear perfect codes over infinite skew fields and quasi skew fields with right (left) unity. A complete classification of such…

cs.IT2022★ 5 cited

A family of diameter perfect constant-weight codes from Steiner systems

Minjia Shi, Yuhong Xia, Denis S. Krotov

If $S$ is a transitive metric space, then $∣ C ∣ \cdot ∣ A ∣ \leq ∣ S ∣$ for any distance- $d$ code $C$ and a set $A$ , ``anticode'', of diameter less than $d$ . For every Steiner S $(t, k, n)$ s…

cs.IT2022★ 3 cited

Constructing MRD codes by switching

Minjia Shi, Denis S. Krotov, Ferruh Özbudak

MRD codes are maximum codes in the rank-distance metric space on $m$ -by- $n$ matrices over the finite field of order $q$ . They are diameter perfect and have the cardinality $q^{m(n-…

cs.IT2021★ 4 cited

An Upper Bound on the Number of Bent Functions

Vladimir N. Potapov

The number of $n$ -ary bent functions is less than $2^{3 \cdot 2^{n - 3} (1 + o (1))}$ as $n$ is even and $n \to \infty$ . Keywords: Boolean function, bent function, upper bound

cs.IT2021

On weight spectrum of linear codes

Vladimir N. Potapov

We study sequences of linear or affine codes with uniform weight spectrum, i.e., a part of codewords with any fixed weight tends to zero. It is proved that a sequence of linear cod…

cs.IT2019★ 4 cited

On q-ary Bent and Plateaued Functions

Vladimir N. Potapov

We obtain the following results. For any prime $q$ the minimal Hamming distance between distinct regular $q$ -ary bent functions of $2 n$ variables is equal to $q^{n}$ . The number of $…

cs.IT2019★ 6 cited

A Lower Bound on the Number of Boolean Functions with Median Correlation Immunity

Vladimir N. Potapov

The number of $n$ -ary balanced correlation immune (resilient) Boolean functions of order $\frac{n}{2}$ is not less than $n^{2^{(n /2) - 2} (1 + o (1))}$ as $n \to \infty$ . Keywords:…

cs.IT2019

On dual codes in the Doob schemes

Denis S. Krotov

The Doob scheme $D (m, n^{'} + n^{''})$ is a metric association scheme defined on $E_{4}^{m} \times F_{4}^{n^{'}} \times Z_{4}^{n^{''}}$ , where $E_{4} = GR (4^{2})$ or, alternatively, on $Z_4^{2m} \times Z_2^{2n'…

cs.IT2018★ 4 cited

The existence of perfect codes in Doob graphs

Denis S. Krotov

We solve the problem of existence of perfect codes in the Doob graph. It is shown that 1-perfect codes in the Doob graph D(m,n) exist if and only if 6m+3n+1 is a power of 2; that i…

cs.IT2018★ 6 cited

A new approach to the Kasami codes of type 2

Minjia Shi, Denis Krotov, Patrick Solé

The dual of the Kasami code of length $q^{2} - 1$ , with $q$ a power of $2$ , is constructed by concatenating a cyclic MDS code of length $q + 1$ over $F_{q}$ with a Simplex code of length $…

cs.IT2018★ 55 cited

On $Z_{p} Z_{p^{k}}$ -additive codes and their duality

Minjia Shi, Rongsheng Wu, Denis S. Krotov

In this paper, two different Gray-like maps from $Z_{p}^{α} \times Z_{p^{k}}^{β}$ , where $p$ is prime, to $Z_{p}^{n}$ , $n = α + β p^{k - 1}$ , denoted by $ϕ$ and $Φ$ , respectively, are presented. We…

cs.IT2018★ 10 cited

Additive perfect codes in Doob graphs

Minjia Shi, Daitao Huang, Denis S. Krotov

The Doob graph $D (m, n)$ is the Cartesian product of $m > 0$ copies of the Shrikhande graph and $n$ copies of the complete graph of order $4$ . Naturally, $D (m, n)$ can be represented a…

cs.IT2017★ 2 cited

On non-full-rank perfect codes over finite fields

Alexander M. Romanov

The paper deals with the perfect 1-error correcting codes over a finite field with $q$ elements (briefly $q$ -ary 1-perfect codes). We show that the orthogonal code to the $q$ -ary n…

cs.IT2016

On the Automorphism Groups of the Z2Z4-Linear 1-Perfect and Preparata-Like Codes

Denis Krotov

We consider the symmetry group of a $Z_{2} Z_{4}$ -linear code with parameters of a $1$ -perfect, extended $1$ -perfect, or Preparata-like code. We show that, provided the code length is g…

cs.IT2015★ 1 cited

On perfect codes that do not contain Preparata-like codes

Denis S. Krotov, Anastasia Yu. Vasil'eva

We show that for every length of form $4^{k} - 1$ , there exists a binary $1$ -perfect code that does not include any Preparata-like code.

cs.IT2014★ 36 cited

On the Classification of MDS Codes

Janne I. Kokkala, Denis S. Krotov, Patric R. J. Östergård

A $q$ -ary code of length $n$ , size $M$ , and minimum distance $d$ is called an $(n, M, d)_{q}$ code. An $(n, q^{k}, n - k + 1)_{q}$ code is called a maximum distance separable (MDS) code. In th…

cs.IT2014★ 22 cited

Classification of the Z2Z4-linear Hadamard codes and their automorphism groups

Denis Krotov, Mercè Villanueva

A $Z_{2} Z_{4}$ -linear Hadamard code of length $α + 2 β = 2^{t}$ is a binary Hadamard code which is the Gray map image of a $Z_{2} Z_{4}$ -additive code with $α$ binary coordinates and $β$ quaternar…

cs.IT2013★ 1 cited

Full-Rank Perfect Codes over Finite Fields

Alexander M. Romanov

In this paper, we propose a construction of full-rank q-ary 1-perfect codes over finite fields. This construction is a generalization of the Etzion and Vardy construction of full-r…

cs.IT2013★ 2 cited

Constructions of transitive latin hypercubes

Denis Krotov, Vladimir Potapov

A function $f : {0, ..., q - 1}^{n} \to {0, ..., q - 1}$ invertible in each argument is called a latin hypercube. A collection $(π_{0}, π_{1}, ..., π_{n})$ of permutations of ${0, ..., q - 1}$ is calle…

cs.IT2013★ 8 cited

Propelinear 1-perfect codes from quadratic functions

Denis Krotov, Vladimir Potapov

Perfect codes obtained by the Vasil'ev--Schönheim construction from a linear base code and quadratic switching functions are transitive and, moreover, propelinear. This gives at le…

cs.IT2012

Self-embeddings of Hamming Steiner triple systems of small order and APN permutations

J. Rifà, F. I. Solov'eva, M. Villanueva

The classification, up to isomorphism, of all self-embedding monomial power permutations of Hamming Steiner triple systems of order n=2^m-1 for small m, m < 23, is given. As far as…

cs.IT2012★ 2 cited

A partition of the hypercube into maximally nonparallel Hamming codes

Denis Krotov

By using the Gold map, we construct a partition of the hypercube into cosets of Hamming codes such that for every two cosets the corresponding Hamming codes are maximally nonparall…

Multispreads

Existence of balanced functions that are not derivative of bent functions

Linear and group perfect codes over skew fields and quasi skew fields

A family of diameter perfect constant-weight codes from Steiner systems

Constructing MRD codes by switching

An Upper Bound on the Number of Bent Functions

On weight spectrum of linear codes

On q-ary Bent and Plateaued Functions

A Lower Bound on the Number of Boolean Functions with Median Correlation Immunity

On dual codes in the Doob schemes

The existence of perfect codes in Doob graphs

A new approach to the Kasami codes of type 2

On Zp​Zpk​-additive codes and their duality

Additive perfect codes in Doob graphs

On non-full-rank perfect codes over finite fields

On the Automorphism Groups of the Z2Z4-Linear 1-Perfect and Preparata-Like Codes

On perfect codes that do not contain Preparata-like codes

On the Classification of MDS Codes

Classification of the Z2Z4-linear Hadamard codes and their automorphism groups

Full-Rank Perfect Codes over Finite Fields

Constructions of transitive latin hypercubes

Propelinear 1-perfect codes from quadratic functions

Self-embeddings of Hamming Steiner triple systems of small order and APN permutations

A partition of the hypercube into maximally nonparallel Hamming codes

On $Z_{p} Z_{p^{k}}$ -additive codes and their duality