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

Showing 2014 · math.COShow all

4 papers · 2 filters

math.CO2014★ 4 cited

Embedding in $q$ -ary $1$ -perfect codes and partitions

Denis S. Krotov, Evgeniya V. Sotnikova

We prove that every $1$ -error-correcting code over a finite field can be embedded in a $1$ -perfect code of some larger length. Embedding in this context means that the original cod…

math.CO2014

On a test on switching separability of graphs modulo $q$

Evgeny Bespalov, Denis Krotov

We consider the graphs whose edges are marked by the integers (weights) from $0$ to $q - 1$ (zero corresponds to no-edge). Such graph is called additive if its vertices can be marked…

math.CO2014★ 29 cited

To the theory of $q$ -ary Steiner and other-type trades

Denis Krotov, Ivan Mogilnykh, Vladimir Potapov

We introduce the concept of a clique bitrade, which generalizes several known types of bitrades, including latin bitrades, Steiner $T (k - 1, k, v)$ bitrades, extended $1$ -perfect bitra…

math.CO2014★ 9 cited

Perfect codes in Doob graphs

Denis Krotov

We study $1$ -perfect codes in Doob graphs $D (m, n)$ . We show that such codes that are linear over $GR (4^{2})$ exist if and only if $n = (4^{g + d} - 1) /3$ and $m = (4^{g + 2 d} - 4^{g + d}) /6$ for s…

Embedding in q-ary 1-perfect codes and partitions

On a test on switching separability of graphs modulo q

To the theory of q-ary Steiner and other-type trades

Perfect codes in Doob graphs

Embedding in $q$ -ary $1$ -perfect codes and partitions

On a test on switching separability of graphs modulo $q$

To the theory of $q$ -ary Steiner and other-type trades