Mathematicshttp://hdl.handle.net/10034/6230132020-08-15T07:52:16Z2020-08-15T07:52:16ZDOMestic Energy Systems and Technologies InCubator (DOMESTIC) and indoor air quality of the built environmentLi, JinghuaKhalid, YousafPhillips, Gavin J.http://hdl.handle.net/10034/6235822020-08-08T01:26:04ZDOMestic Energy Systems and Technologies InCubator (DOMESTIC) and indoor air quality of the built environment
Li, Jinghua; Khalid, Yousaf; Phillips, Gavin J.
Oral presentation at RMetS Students and Early Career Scientists Conference 2020 on research project DOMESTIC (DOMestic Energy Systems and Technologies InCubator), which aims to build a facility for the demonstration of domestic technologies and design methodologies (i.e. air quality, energy efficiency).
New Self-Dual Codes of Length 68 from a 2 × 2 Block Matrix Construction and Group RingsBortos, MariaGildea, JoeKaya, AbidinKorban, AdrianTylyshchak, Alexanderhttp://hdl.handle.net/10034/6235792020-08-08T01:25:28ZNew Self-Dual Codes of Length 68 from a 2 × 2 Block Matrix Construction and Group Rings
Bortos, Maria; Gildea, Joe; Kaya, Abidin; Korban, Adrian; Tylyshchak, Alexander
Many generator matrices for constructing extremal binary self-dual codes of different
lengths have the form G = (In | A); where In is the n x n identity matrix and A is
the n x n matrix fully determined by the first row. In this work, we define a generator
matrix in which A is a block matrix, where the blocks come from group rings and also,
A is not fully determined by the elements appearing in the first row. By applying our
construction over F2 +uF2 and by employing the extension method for codes, we were
able to construct new extremal binary self-dual codes of length 68. Additionally, by
employing a generalised neighbour method to the codes obtained, we were able to con-
struct many new binary self-dual [68,34,12]-codes with the rare parameters
$\gamma = 7$; $8$ and $9$ in $W_{68,2}$: In particular, we find 92 new binary
self-dual [68,34,12]-codes.
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Advances in Mathematics of Communications following peer review. The definitive publisher-authenticated version Bortos, M., Gildea, J., Kaya, A., Korban, A. & Tylyshchak,A. (2020-forthcoming). New Self-Dual Codes of length 68 from a 2 × 2 block matrix Construction and Group Rings. Advances in Mathematics of Communications. is available online at: URL/DOI to be added on publication.
Self-Dual Codes using Bisymmetric Matrices and Group RingsGildea, JoeKaya, AbidinKorban, AdrianTylyshchak, Alexanderhttp://hdl.handle.net/10034/6235602020-07-30T01:13:02ZSelf-Dual Codes using Bisymmetric Matrices and Group Rings
Gildea, Joe; Kaya, Abidin; Korban, Adrian; Tylyshchak, Alexander
In this work, we describe a construction in which we combine together the idea of a
bisymmetric matrix and group rings. Applying this construction over the ring F4 + uF4 together
with the well known extension and neighbour methods, we construct new self-dual codes of length
68: In particular, we find 41 new codes of length 68 that were not known in the literature before.
New Extremal binary self-dual codes of length 68 from generalized neighborsGildea, JoeKaya, AbidinKorban, AdrianYildiz, Bahattinhttp://hdl.handle.net/10034/6235552020-07-23T01:11:09ZNew Extremal binary self-dual codes of length 68 from generalized neighbors
Gildea, Joe; Kaya, Abidin; Korban, Adrian; Yildiz, Bahattin
In this work, we use the concept of distance between self-dual codes, which generalizes the concept of a neighbor for self-dual codes. Using the $k$-neighbors, we are able to construct extremal binary self-dual codes of length 68 with new weight enumerators. We construct 143 extremal binary self-dual codes of length 68 with new weight enumerators including 42 codes with $\gamma=8$ in their $W_{68,2}$ and 40 with $\gamma=9$ in their $W_{68,2}$. These examples are the first in the literature for these $\gamma$ values. This completes the theoretical list of possible values for $\gamma$ in $W_{68,2}$.