Zobrazeno 1 - 10
of 17
pro vyhledávání: '"Alexander Tylyshchak"'
Publikováno v:
Advances in Mathematics of Communications. 17:1086-1100
In this paper, we construct new self-dual codes from a construction that involves a unique combination; \begin{document}$ 2 \times 2 $\end{document} block circulant matrices, group rings and a reverse circulant matrix. There are certain conditions, s
Publikováno v:
Науковий вісник Ужгородського університету. Серія: Математика і інформатика. 40:27-32
Для побудови лінійних бінарних самодуальних кодів було встановлено багато різних конструкцій. У статті розглядаємо побудову розширени
Autor:
Alexander Tylyshchak
Publikováno v:
Journal of Mathematical Sciences. 258:455-465
The series of indecomposable modular representations of a cyclic p -group a over a commutative local nonintegral ring of principal ideals of characteristic p is constructed in the form a → E + M , where E is the identity matrix and M is a monomial
Autor:
Alexander Tylyshchak, M. Demko
Publikováno v:
Carpathian Mathematical Publications. 13:127-133
Розглядаються мономіальні матриці над локальним кільцем $R$ головних ідеалів вигляду $M(t,k,n)=\Phi\left(\begin{smallmatrix}I_k&0\\0\,\,&tI_{n-k}\end{smallmatrix}\right)$, $0
Publikováno v:
Cryptography and Communications. 12:769-784
In this work, we describe a double bordered construction of self-dual codes from group rings. We show that this construction is effective for groups of order 2p where p is odd, over the rings $\mathbb {F}_{2}+u\mathbb {F}_{2}$ F 2 + u F 2 and $\mathb
Autor:
Alexander Tylyshchak
Publikováno v:
Ukrainian Mathematical Journal. 71:1312-1319
It is proved that all maximal unipotent subgroups of a special linear group over commutative ring with identity (such that the factor ring of its modulo primitive radical is a finite direct sum of Bezout domains) are pairwise conjugated and describe
Autor:
Bahattin Yildiz, Alexander Tylyshchak, Joe Gildea, Abidin Kaya, Adrian Korban, Steven T. Dougherty
Publikováno v:
Finite Fields and Their Applications. 57:108-127
We introduce a bordered construction over group rings for self-dual codes. We apply the constructions over the binary field and the ring F 2 + u F 2 , using groups of orders 9, 15, 21, 25, 27, 33 and 35 to find extremal binary self-dual codes of leng
Publikováno v:
Advances in Mathematics of Communications. 16:269
Many generator matrices for constructing extremal binary self-dual codes of different lengths have the form \begin{document}$ G = (I_n \ | \ A), $\end{document} where \begin{document}$ I_n $\end{document} is the \begin{document}$ n \times n $\end{doc
In this paper, we construct self-dual codes from a construction that involves both block circulant matrices and block quadratic residue circulant matrices. We provide conditions when this construction can yield self-dual codes. We construct self-dual
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2b1b494aeea19ce95e8bbb7c483a55b8
Publikováno v:
Designs, Codes and Cryptography. 86:2115-2138
We describe G-codes, which are codes that are ideals in a group ring, where the ring is a finite commutative Frobenius ring and G is an arbitrary finite group. We prove that the dual of a G-code is also a G-code. We give constructions of self-dual an