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

78 papers

math.CO2024

Triangle decompositions of PG(n-1,2)

Minjia Shi, Xiaoxiao Li, Denis S. Krotov

We define a triangle design as a partition of the set of lines of a projective space into triangles, where a triangle consists of three pairwise intersecting lines with no common p…

math.CO2023★ 3 cited

Quasi-cyclic perfect codes in Doob graphs and special partitions of Galois rings

Minjia Shi, Xiaoxiao Li, Denis S. Krotov +1

The Galois ring GR $(4^{Δ})$ is the residue ring $Z_{4} [x] / (h (x))$ , where $h (x)$ is a basic primitive polynomial of degree $Δ$ over $Z_{4}$ . For any odd $Δ$ larger than $1$ , we construct…

math.CO2023

Do $K_{3, 3}$ -Free Latin Squares Exist?

Aleksandr D. Krotov, Denis S. Krotov

We discuss the problem of the existence of latin squares without a substructure consisting of six elements $(r_{1}, c_{2}, l_{3})$ , $(r_{2}, c_{3}, l_{1})$ , $(r_{3}, c_{1}, l_{2})$ , $(r_{2}, c_{1}, l_{3})$ , $(r_3…

math.CO2022

An upper bound on the number of frequency hypercubes

Denis S. Krotov, Vladimir N. Potapov

A frequency $n$ -cube $F^{n} (q; l_{0}, ..., l_{m - 1})$ is an $n$ -dimensional $q$ -by-...-by- $q$ array, where $q = l_{0} + ... + l_{m - 1}$ , filled by numbers $0, ..., m - 1$ with the property that each…

math.CO2022★ 3 cited

Multifold 1-perfect codes

Denis S. Krotov

A multifold $1$ -perfect code ( $1$ -perfect code for list decoding) in any graph is a set $C$ of vertices such that every vertex of the graph is at distance not more than $1$ from ex…

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…