Zobrazeno 1 - 10
of 283
pro vyhledávání: '"Krotov, Denis"'
Autor:
Goryainov, Sergey, Krotov, Denis
In Cayley graphs on the additive group of a small vector space over GF$(q)$, $q=2,3$, we look for completely regular (CR) codes whose parameters are new in Hamming graphs over the same field. The existence of a CR code in such Cayley graph $G$ implie
Externí odkaz:
http://arxiv.org/abs/2411.09698
We define a triangle design as a partition of the set of $2$-dimensional subspaces of an $n$-dimensional vector space into triangles, where a triangle consists of three subspaces with the trivial, $0$-dimensional, intersection and $1$-dimensional mut
Externí odkaz:
http://arxiv.org/abs/2407.19157
Autor:
Krotov, Denis S.
We solve several first questions in the table of small parameters of completely regular (CR) codes in Hamming graphs $H(n,q)$. The most uplifting result is the existence of a $\{13,6,1;1,6,9\}$-CR code in $H(n,2)$, $n\ge 13$. We also establish the no
Externí odkaz:
http://arxiv.org/abs/2312.08360
Autor:
Krotov, Denis S., Mogilnykh, Ivan Yu.
Additive one-weight codes over a finite field of non-prime order are equivalent to special subspace coverings of the points of projective space, which we call multispreads. The current paper is devoted to the characterization of the parameters of mul
Externí odkaz:
http://arxiv.org/abs/2312.07883
Publikováno v:
Discrete Math. 347(10) 2024, 114138(1-14)
A perfect $k$-coloring of the Boolean hypercube $Q_n$ is a function from the set of binary words of length $n$ onto a $k$-set of colors such that for any colors $i$ and $j$ every word of color $i$ has exactly $S(i,j)$ neighbors (at Hamming distance $
Externí odkaz:
http://arxiv.org/abs/2311.05566
Autor:
Krotov, Denis S.
Publikováno v:
Discrete Math. 347(5) 2024, 113923(1-8)
We describe the classification of orthogonal arrays OA$(2048,14,2,7)$, or, equivalently, completely regular $\{14;2\}$-codes in the $14$-cube ($30848$ equivalence classes). In particular, we find that there is exactly one almost-OA$(2048,14,2,7{+}1)$
Externí odkaz:
http://arxiv.org/abs/2311.05428
Publikováno v:
IEEE Trans. Inf. Theory 69(9) 2023, 5597-5603
The Galois ring GR$(4^\Delta)$ is the residue ring $Z_4[x]/(h(x))$, where $h(x)$ is a basic primitive polynomial of degree $\Delta$ over $Z_4$. For any odd $\Delta$ larger than $1$, we construct a partition of GR$(4^\Delta) \backslash \{0\}$ into $6$
Externí odkaz:
http://arxiv.org/abs/2305.02735
Autor:
Krotov, Aleksandr D., Krotov, Denis S.
We discuss the problem of existence of latin squares without a substructure consisting of six elements $(r_1,c_2,l_3)$, $(r_2,c_3,l_1)$, $(r_3,c_1,l_2)$, $(r_2,c_1,l_3)$, $(r_3,c_2,l_1)$, $(r_1,c_3,l_2)$. Equivalently, the corresponding latin square
Externí odkaz:
http://arxiv.org/abs/2304.07157
Autor:
Krotov, Denis S., Potapov, Vladimir N.
Publikováno v:
Discrete Math. 347(1) 2024, 113657(1-9)
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 line contains exactly $l_i$ cells with symbol $i$, $i = 0,...,m-1$ (a
Externí odkaz:
http://arxiv.org/abs/2212.03694
Autor:
Krotov, Denis S.
Publikováno v:
J. Comb. Des. 32(9) 2024, 546-555
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 exactly $\mu$ elements of $C$. In $q$-ary Hamming graphs, where $q$ is a
Externí odkaz:
http://arxiv.org/abs/2212.03644