Zobrazeno 1 - 8
of 8
pro vyhledávání: '"Rhian Taylor"'
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:
New Zealand Journal of Marine and Freshwater Research. 56:291-302
This study assessed the potential of the mud snail Amphibola crenata as a bioindicator of estuarine health. Multiple sites with varying contaminant inputs were identified within a small, shallow es...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::db0570fb935c36a083d494fcbc5cac83
https://doi.org/10.1080/00288330.2021.1929350
https://doi.org/10.1080/00288330.2021.1929350
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
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:
Finite Fields and Their Applications. 51:71-92
In this work, we establish a strong connection between group rings and self-dual codes. We prove that a group ring element corresponds to a self-dual code if and only if it is a unitary unit. We also show that the double-circulant and four-circulant
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::62722ef748db8498dfb95e80e64028ce
https://doi.org/10.1016/j.ffa.2018.01.002
https://doi.org/10.1016/j.ffa.2018.01.002
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
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e2856034d52e5c8ce4adb19790cb20b0
https://doi.org/10.1007/s10623-017-0440-7
https://doi.org/10.1007/s10623-017-0440-7
Autor:
Rhian Taylor, Joe Gildea
Publikováno v:
Volume: 24, Issue: 24 62-67
International Electronic Journal of Algebra
International Electronic Journal of Algebra
In this paper, we establish the structure of the unit group of the group algebra.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::60bb09aeb760770a65f471b796f479d7
https://doi.org/10.24330/ieja.440205
https://doi.org/10.24330/ieja.440205