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## A modified bordered construction for self-dual codes from group rings

#### Joe GILDEA [1] , Abidin KAYA [2] , Alexander TYLYSHCHAK [3] , Bahattin YILDIZ [4]

We describe a bordered construction for self-dual codes coming from group rings. We apply the constructions coming from the cyclic and dihedral groups over several alphabets to obtain extremal binary self-dual codes of various lengths. In particular we find a new extremal binary self-dual code of length 78.
Group rings, Self-dual codes, Codes over rings, Bordered constructions
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Primary Language en Engineering Articles Author: Joe GILDEA Institution: University of ChesterCountry: United Kingdom Orcid: 0000-0003-0175-1909Author: Abidin KAYA Institution: Sampoerna UniversityCountry: Indonesia Author: Alexander TYLYSHCHAK Institution: Uzhgorod State UniversityCountry: Ukraine Orcid: 0000-0001-8106-3123Author: Bahattin YILDIZ Institution: Northern Arizona UniversityCountry: United States Publication Date : May 7, 2020
 Bibtex @research article { jacodesmath729402, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2020}, volume = {7}, pages = {103 - 119}, doi = {10.13069/jacodesmath.729402}, title = {A modified bordered construction for self-dual codes from group rings}, key = {cite}, author = {Gıldea, Joe and Kaya, Abidin and Tylyshchak, Alexander and Yıldız, Bahattin} } APA Gıldea, J , Kaya, A , Tylyshchak, A , Yıldız, B . (2020). A modified bordered construction for self-dual codes from group rings . Journal of Algebra Combinatorics Discrete Structures and Applications , 7 (2) , 103-119 . DOI: 10.13069/jacodesmath.729402 MLA Gıldea, J , Kaya, A , Tylyshchak, A , Yıldız, B . "A modified bordered construction for self-dual codes from group rings" . Journal of Algebra Combinatorics Discrete Structures and Applications 7 (2020 ): 103-119 Chicago Gıldea, J , Kaya, A , Tylyshchak, A , Yıldız, B . "A modified bordered construction for self-dual codes from group rings". Journal of Algebra Combinatorics Discrete Structures and Applications 7 (2020 ): 103-119 RIS TY - JOUR T1 - A modified bordered construction for self-dual codes from group rings AU - Joe Gıldea , Abidin Kaya , Alexander Tylyshchak , Bahattin Yıldız Y1 - 2020 PY - 2020 N1 - doi: 10.13069/jacodesmath.729402 DO - 10.13069/jacodesmath.729402 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 103 EP - 119 VL - 7 IS - 2 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.729402 UR - https://doi.org/10.13069/jacodesmath.729402 Y2 - 2019 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications A modified bordered construction for self-dual codes from group rings %A Joe Gıldea , Abidin Kaya , Alexander Tylyshchak , Bahattin Yıldız %T A modified bordered construction for self-dual codes from group rings %D 2020 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 7 %N 2 %R doi: 10.13069/jacodesmath.729402 %U 10.13069/jacodesmath.729402 ISNAD Gıldea, Joe , Kaya, Abidin , Tylyshchak, Alexander , Yıldız, Bahattin . "A modified bordered construction for self-dual codes from group rings". Journal of Algebra Combinatorics Discrete Structures and Applications 7 / 2 (May 2020): 103-119 . https://doi.org/10.13069/jacodesmath.729402 AMA Gıldea J , Kaya A , Tylyshchak A , Yıldız B . A modified bordered construction for self-dual codes from group rings. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020; 7(2): 103-119. Vancouver Gıldea J , Kaya A , Tylyshchak A , Yıldız B . A modified bordered construction for self-dual codes from group rings. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020; 7(2): 103-119.

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