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pro vyhledávání: '"Mogilnykh, Ivan"'
Autor:
Marin, Alexey D., Mogilnykh, Ivan Yu.
In this paper, we study the minimum distances of binary linear codes with parity check matrices formed from subset inclusion matrices $W_{t,n,k}$, representing $t$-element subsets versus $k$-element subsets of an $n$-element set. We provide both lowe
Externí odkaz:
http://arxiv.org/abs/2408.12154
We obtain a classification of the completely regular codes with covering radius 1 and the second eigenvalue in the Hamming graphs H(3,q) up to q and intersection array. Due to works of Meyerowitz, Mogilnykh and Valyuzenich, our result completes the c
Externí odkaz:
http://arxiv.org/abs/2403.02702
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:
In Discrete Mathematics February 2025 348(2)
Autor:
Mogilnykh, Ivan
We propose a new method of constructing q-ary propelinear perfect codes. The approach utilizes permutations of the fixed length q-ary vectors that arise from the automorphisms of the regular subgroups of the affine group. For any prime q it is shown
Externí odkaz:
http://arxiv.org/abs/2112.08659
The eigenvalues of the Hamming graph $H(n,q)$ are known to be $\lambda_i(n,q)=(q-1)n-qi$, $0\leq i \leq n$. The characterization of equitable 2-partitions of the Hamming graphs $H(n,q)$ with eigenvalue $\lambda_{1}(n,q)$ was obtained by Meyerowitz in
Externí odkaz:
http://arxiv.org/abs/1903.12333
Autor:
Mogilnykh, Ivan
The Star graph $S_n$ is the Cayley graph of the symmetric group $Sym_n$ with the generating set $\{(1\mbox{ }i): 2\leq i\leq n \}$. Arumugam and Kala proved that $\{\pi\in Sym_n: \pi(1)=1\}$ is a perfect code in $S_n$ for any $n, n\geq 3$. In this no
Externí odkaz:
http://arxiv.org/abs/1903.08824
We consider constructions of covering-radius-1 completely regular codes, or, equivalently, equitable 2-partitions (regular 2-partitions, perfect 2-colorings), of halved n-cubes. Keywords: completely regular code, equitable partition, regular partitio
Externí odkaz:
http://arxiv.org/abs/1812.03159
We study the weights of eigenvectors of the Johnson graphs $J(n,w)$. For any $i \in \{1,\ldots,w\}$ and sufficiently large $n, n\geq n(i,w)$ we show that an eigenvector of $J(n,w)$ with the eigenvalue $\lambda_i=(n-w-i)(w-i)-i$ has at least $2^i(^{n-
Externí odkaz:
http://arxiv.org/abs/1706.03987
Publikováno v:
In Discrete Mathematics November 2020 343(11)