Show simple item record

dc.contributor.authorDougherty, Steven
dc.contributor.authorGildea, Joe
dc.contributor.authorKorban, Adrian
dc.contributor.authorSahinkaya, Serap
dc.date.accessioned2021-03-29T10:41:42Z
dc.date.available2021-03-29T10:41:42Z
dc.identifierhttps://chesterrep.openrepository.com/bitstream/handle/10034/624410/B_%7bj%2ck%7dRevised.pdf?sequence=1
dc.identifier.citationDougherty, S., Gildea, J., Korban, A., & Sahinkaya, S. (2021). G-Codes, self-dual G-Codes and reversible G-Codes over the Ring Bj,k. Cryptography and Communications (awaiting publication).en_US
dc.identifier.urihttp://hdl.handle.net/10034/624410
dc.descriptionThe final publication is available at Springer via http://dx.doi.org/[insert DOI]”en_US
dc.description.abstractIn this work, we study a new family of rings, Bj,k, whose base field is the finite field Fpr . We study the structure of this family of rings and show that each member of the family is a commutative Frobenius ring. We define a Gray map for the new family of rings, study G-codes, self-dual G-codes, and reversible G-codes over this family. In particular, we show that the projection of a G-code over Bj,k to a code over Bl,m is also a G-code and the image under the Gray map of a self-dual G-code is also a self-dual G-code when the characteristic of the base field is 2. Moreover, we show that the image of a reversible G-code under the Gray map is also a reversible G2j+k-code. The Gray images of these codes are shown to have a rich automorphism group which arises from the algebraic structure of the rings and the groups. Finally, we show that quasi-G codes, which are the images of G-codes under the Gray map, are also Gs-codes for some s.en_US
dc.publisherSpringeren_US
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/en_US
dc.subjectcodes over ringsen_US
dc.subjectGray mapsen_US
dc.subjectself-dual codesen_US
dc.titleG-Codes, self-dual G-Codes and reversible G-Codes over the Ring Bj,ken_US
dc.typeArticleen_US
dc.identifier.eissn1936-2455en_US
dc.contributor.departmentTarsus University; University of Chesteren_US
dc.identifier.journalCryptography and Communicationsen_US
or.grant.openaccessYesen_US
rioxxterms.funderunfundeden_US
rioxxterms.identifier.projectunfundeden_US
rioxxterms.versionAMen_US
rioxxterms.licenseref.startdate2022-12-31
dcterms.dateAccepted2021-03-24
rioxxterms.publicationdate2021-03
dc.date.deposited2021-03-29en_US
dc.indentifier.issn1936-2447en_US


Files in this item

Thumbnail
Name:
B_{j,k}Revised.pdf
Embargo:
2022-12-31
Size:
347.6Kb
Format:
PDF
Request:
Main article

This item appears in the following Collection(s)

Show simple item record

https://creativecommons.org/licenses/by-nc-nd/4.0/
Except where otherwise noted, this item's license is described as https://creativecommons.org/licenses/by-nc-nd/4.0/