9 citations · 10 across the 8 of their papers we have counts for
8 papers · 1 filter
The punctured dodecacode is unique
Markus Grassl, Denis Krotov, Lin Sok +1
The punctured dodecacode is an additive -ary code of length and distance which is uniformly packed. We show that a code with the same weight distribution is equivalent…
Generalized ovals, 2.5-dimensional additive codes, and multispreads
Denis S. Krotov, Sascha Kurz
We present constructions and bounds for additive codes over a finite field in terms of their geometric counterpart, i.e., projective systems. It is known that the maximum number of…
The spectral Turán problem: Characterizing spectral-consistent graphs
Longfei Fang, Sergey Goryainov, Denis Krotov +2
Let and denote the families of -free graphs of order with maximum size and maximum spectral radius, respectively. A graph is called spe…
Maximum Size -Intersecting Families and Anticodes
Xuan Wang, Tuvi Etzion, Denis Krotov +1
The maximum size of -intersecting families is one of the most celebrated topics in combinatorics, and its size is known as the Erdős-Ko-Rado theorem. Such intersecting families,…
Completely regular codes in graphs covered by a Hamming graph
Sergey Goryainov, Denis Krotov
In Cayley graphs on the additive group of a small vector space over GF, , we look for completely regular (CR) codes whose parameters are new in Hamming graphs over the…
On the existence of some completely regular codes in Hamming graphs
Denis S. Krotov
We solve several first questions in the table of small parameters of completely regular (CR) codes in Hamming graphs . The most uplifting result is the existence of a $\{13…
On degree- and -correlation-immune perfect colorings of -cubes
Denis S. Krotov, Alexandr A. Valyuzhenich
A perfect -coloring of the Boolean hypercube is a function from the set of binary words of length onto a -set of colors such that for any colors and every w…
On the number of n-ary quasigroups of finite order
Denis Krotov, Vladimir Potapov
Let be the number of -ary quasigroups of order . We derive a recurrent formula for Q(n,4). We prove that for all and the following inequalities h…