Zobrazeno 1 - 10
of 225
pro vyhledávání: '"Solov'eva, A. I."'
Autor:
Mogilnykh, I. Yu., Solov'eva, F. I.
Publikováno v:
Siberian Electronic Mathematical Reports 17 (2020), 1451-1462
We continue the study of the class of binary extended perfect propelinear codes constructed in the previous paper and consider their permutation automorphism (symmetry) groups and Steiner quadruple systems. We show that the automorphism group of the
Externí odkaz:
http://arxiv.org/abs/2009.08191
Autor:
Mogilnykh, I. Yu., Solov'eva, F. I.
A pair $(T_0,T_1)$ of disjoint sets of vertices of a graph $G$ is called a perfect bitrade in $G$ if any ball of radius 1 in $G$ contains exactly one vertex in $T_0$ and $T_1$ or none simultaneously. The volume of a perfect bitrade $(T_0,T_1)$ is the
Externí odkaz:
http://arxiv.org/abs/1912.09089
Autor:
Mogilnykh, I. Yu., Solov'eva, F. I.
A code $C$ is called propelinear if there is a subgroup of $Aut(C)$ of order $|C|$ acting transitively on the codewords of $C$. In the paper new propelinear perfect binary codes of any admissible length more than $7$ are obtained by a particular case
Externí odkaz:
http://arxiv.org/abs/1905.10005
Autor:
Solov'eva, Faina I.
We investigate transitive uniform partitions of the vector space $F^n$ of dimension $n$ over the Galois field $GF(2)$ into cosets of Hamming codes. A partition $P^n= \{H_0,H_1+e_1,\ldots,H_n+e_n\}$ of $F^n$ into cosets of Hamming codes $H_0,H_1,\ldot
Externí odkaz:
http://arxiv.org/abs/1904.01282
Autor:
Mogilnykh, I. Yu., Solov'eva, F. I.
In the paper we investigate the structure of $i$-components of two classes of codes: Kerdock codes and the duals of the primitive cyclic BCH code with designed distance 5 of length $n=2^m-1$, for odd $m$. We prove that for any admissible length a pun
Externí odkaz:
http://arxiv.org/abs/1810.04367
Autor:
Mogilnykh, I. Yu., Solov'eva, F. I.
In the paper we show the existence of a large class of extended perfect binary codes containing maximum ij-components.
Comment: The paper is in Russian. submitted to Sibirian Electronic Mathematical Reports
Comment: The paper is in Russian. submitted to Sibirian Electronic Mathematical Reports
Externí odkaz:
http://arxiv.org/abs/1512.03242
Autor:
Mogilnykh, I. Yu., Solov'eva, F. I.
Studying binary perfect codes we show the existence of homogeneous nontransitive codes. Thus, as far as perfect codes are concerned, the propelinear codes are strictly contained in transitive codes, wheresas homogeneous codes form a strict subclass o
Externí odkaz:
http://arxiv.org/abs/1412.3006
Autor:
Mogilnykh, I. Yu., Solov'eva, F. I.
A code is called transitive if its automorphism group (the isometry group) of the code acts transitively on its codewords. If there is a subgroup of the automorphism group acting regularly on the code, the code is called propelinear. Using Magma soft
Externí odkaz:
http://arxiv.org/abs/1411.2692
The paper proves that there exist an exponential number of nonequivalent propelinear extended perfect binary codes of length growing to infinity. Specifically, it is proved that all transitive extended perfect binary codes found by Potapov are propel
Externí odkaz:
http://arxiv.org/abs/1303.0680
The classification, up to isomorphism, of all self-embedding monomial power permutations of Hamming Steiner triple systems of order n=2^m-1 for small m, m < 23, is given. As far as we know, for m in {5,7,11,13,17,19}, all given self-embeddings in clo
Externí odkaz:
http://arxiv.org/abs/1212.5789