D. Krotov

activity

20052024

most citedOn

Z_{p} Z_{p^{k}}

-additive codes and their duality

55 citations · 628 across the 77 of their papers we have counts for

collaborators

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19 papers · 1 filter

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.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.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★ 2 cited

Non-existence of a ternary constant weight $(16, 5, 15; 2048)$ diameter perfect code

Denis S. Krotov, Patric R. J. Östergård, Olli Pottonen

Ternary constant weight codes of length $n = 2^{m}$ , weight $n - 1$ , cardinality $2^{n}$ and distance $5$ are known to exist for every $m$ for which there exists an APN permutation of orde…

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★ 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★ 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…

cs.IT2011★ 10 cited

On Optimal Binary One-Error-Correcting Codes of Lengths $2^{m} - 4$ and $2^{m} - 3$

Denis S. Krotov, Patric R. J. Östergård, Olli Pottonen

Best and Brouwer [Discrete Math. 17 (1977), 235-245] proved that triply-shortened and doubly-shortened binary Hamming codes (which have length $2^{m} - 4$ and $2^{m} - 3$ , respectively) ar…

cs.IT2009★ 15 cited

On the structure of non-full-rank perfect codes

Denis Krotov, Olof Heden

The Krotov combining construction of perfect 1-error-correcting binary codes from 2000 and a theorem of Heden saying that every non-full-rank perfect 1-error-correcting binary code…

cs.IT2007★ 54 cited

Z4-linear Hadamard and extended perfect codes

Denis Krotov

If $N = 2^{k} > 8$ then there exist exactly $[(k - 1) /2]$ pairwise nonequivalent $Z_{4}$ -linear Hadamard $(N, 2 N, N /2)$ -codes and $[(k + 1) /2]$ pairwise nonequivalent $Z_{4}$ -linear extended per…

cs.IT2007★ 21 cited

Z4-Linear Perfect Codes

Denis Krotov

For every $n = 2^{k} > 8$ there exist exactly $[(k + 1) /2]$ mutually nonequivalent $Z_{4}$ -linear extended perfect codes with distance 4. All these codes have different ranks.

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

Constructing MRD codes by switching

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 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

Non-existence of a ternary constant weight (16,5,15;2048) diameter perfect code

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

Constructions of transitive latin hypercubes

Propelinear 1-perfect codes from quadratic functions

A partition of the hypercube into maximally nonparallel Hamming codes

On Optimal Binary One-Error-Correcting Codes of Lengths 2m−4 and 2m−3

On the structure of non-full-rank perfect codes

Z4-linear Hadamard and extended perfect codes

Z4-Linear Perfect Codes

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

Non-existence of a ternary constant weight $(16, 5, 15; 2048)$ diameter perfect code

On Optimal Binary One-Error-Correcting Codes of Lengths $2^{m} - 4$ and $2^{m} - 3$