Zobrazeno 1 - 10
of 42
pro vyhledávání: '"Joe Gildea"'
Autor:
Joe Gildea
Publikováno v:
International Journal of Group Theory, Vol 6, Iss 1, Pp 37-53 (2017)
In this paper, we investigate the Zassenhaus conjecture for $PSL(4,3)$ and $PSL(5,2)$. Consequently, we prove that the Prime graph question is true for both groups.
Externí odkaz:
https://doaj.org/article/f95b9a41fe1143c891dd34dd85d67389
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
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1741b6d6e9d26a4d88025be2729d5727
https://doi.org/10.3934/amc.2021039
https://doi.org/10.3934/amc.2021039
Publikováno v:
Cryptography and Communications. 13:601-616
In this work, we study a new family of rings, ${\mathscr{B}}_{j,k}$ B j , k , whose base field is the finite field ${\mathbb {F}}_{p^{r}}$ F p r . We study the structure of this family of rings and show that each member of the family is a commutative
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bafea8f3e21d4063f4e44ce61b7aa1a4
https://doi.org/10.1007/s12095-021-00487-x
https://doi.org/10.1007/s12095-021-00487-x
Publikováno v:
International Journal of Algebra and Computation. 31:471-490
In this work, we extend an established isomorphism between group rings and a subring of the [Formula: see text] matrices. This extension allows us to construct more complex matrices over the ring [Formula: see text] We present many interesting exampl
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::aa2389aaa17e7b0a05836c673d1cf469
https://doi.org/10.1142/s0218196721500223
https://doi.org/10.1142/s0218196721500223
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 $\mathb
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b42b76025241fd34a46be53aee8c5609
https://doi.org/10.1007/s12095-019-00420-3
https://doi.org/10.1007/s12095-019-00420-3
Publikováno v:
Advances in Mathematics of Communications. 14:677-702
We describe eight composite constructions from group rings where the orders of the groups are 4 and 8, which are then applied to find self-dual codes of length 16 over \begin{document}$ \mathbb{F}_4 $\end{document} . These codes have binary images wi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::609df3f2580c25aecb1d4054475507c0
https://doi.org/10.3934/amc.2020037
https://doi.org/10.3934/amc.2020037
Publikováno v:
Advances in Mathematics of Communications. 14:11-22
In this work, we study construction methods for self-dual and formally self-dual codes from group rings, arising from the cyclic group, the dihedral group, the dicyclic group and the semi-dihedral group. Using these constructions over the rings \begi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::72fdd68bb10c68f8d214eb397951ca57
https://doi.org/10.3934/amc.2020002
https://doi.org/10.3934/amc.2020002
In this paper, we give a new method for constructing LCD codes. We employ group rings and a well known map that sends group ring elements to a subring of the $n \times n$ matrices to obtain LCD codes. Our construction method guarantees that our LCD c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f8bf6b9da1853bc9d3e2ba92f708d403
http://arxiv.org/abs/2108.05056
http://arxiv.org/abs/2108.05056
Publikováno v:
Cryptography and Communications. 12:127-146
In this paper, we introduce a new bordered construction for self-dual codes using group rings. We consider constructions over the binary field, the family of rings Rk and the ring $\mathbb {F}_{4}+u\mathbb {F}_{4}$. We use groups of order 4, 12 and 2
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3adc7f12ee83d4e7e5bada86211d1e99
https://doi.org/10.1007/s12095-019-00380-8
https://doi.org/10.1007/s12095-019-00380-8
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
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::125d8383722567a81f9669e4464cc39d
https://doi.org/10.1016/j.ffa.2019.02.004
https://doi.org/10.1016/j.ffa.2019.02.004