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## New extremal singly even self-dual codes of lengths 64 and 66

#### Damyan Anev [1] , Masaaki Harada [2] , Nikolay Yankov [3]

For lengths $64$ and $66$, we construct six and seven extremal singly even self-dual codes with weight enumerators for which no extremal singly even self-dual codes were previously known to exist, respectively. We also construct new $40$ inequivalent extremal doubly even self-dual $[64,32,12]$ codes with covering radius $12$ meeting the Delsarte bound. These new codes are constructed by considering four-circulant codes along with their neighbors and shadows.
Self-dual code, Weight enumerator
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Birincil Dil en Mühendislik Makaleler Orcid: 0000-0002-3175-0168Yazar: Damyan Anev Orcid: 0000-0002-2748-6456Yazar: Masaaki Harada (Sorumlu Yazar) Orcid: 0000-0003-3703-5867Yazar: Nikolay Yankov Yayımlanma Tarihi : 8 Ekim 2018
 Bibtex @araştırma makalesi { jacodesmath458601, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yıldız Teknik Üniversitesi}, year = {2018}, volume = {5}, pages = {143 - 151}, doi = {10.13069/jacodesmath.458601}, title = {New extremal singly even self-dual codes of lengths 64 and 66}, key = {cite}, author = {Anev, Damyan and Harada, Masaaki and Yankov, Nikolay} } APA Anev, D , Harada, M , Yankov, N . (2018). New extremal singly even self-dual codes of lengths 64 and 66. Journal of Algebra Combinatorics Discrete Structures and Applications , 5 (3) , 143-151 . DOI: 10.13069/jacodesmath.458601 MLA Anev, D , Harada, M , Yankov, N . "New extremal singly even self-dual codes of lengths 64 and 66". Journal of Algebra Combinatorics Discrete Structures and Applications 5 (2018 ): 143-151 Chicago Anev, D , Harada, M , Yankov, N . "New extremal singly even self-dual codes of lengths 64 and 66". Journal of Algebra Combinatorics Discrete Structures and Applications 5 (2018 ): 143-151 RIS TY - JOUR T1 - New extremal singly even self-dual codes of lengths 64 and 66 AU - Damyan Anev , Masaaki Harada , Nikolay Yankov Y1 - 2018 PY - 2018 N1 - doi: 10.13069/jacodesmath.458601 DO - 10.13069/jacodesmath.458601 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 143 EP - 151 VL - 5 IS - 3 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.458601 UR - https://doi.org/10.13069/jacodesmath.458601 Y2 - 2018 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications New extremal singly even self-dual codes of lengths 64 and 66 %A Damyan Anev , Masaaki Harada , Nikolay Yankov %T New extremal singly even self-dual codes of lengths 64 and 66 %D 2018 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 5 %N 3 %R doi: 10.13069/jacodesmath.458601 %U 10.13069/jacodesmath.458601 ISNAD Anev, Damyan , Harada, Masaaki , Yankov, Nikolay . "New extremal singly even self-dual codes of lengths 64 and 66". Journal of Algebra Combinatorics Discrete Structures and Applications 5 / 3 (Ekim 2018): 143-151 . https://doi.org/10.13069/jacodesmath.458601 AMA Anev D , Harada M , Yankov N . New extremal singly even self-dual codes of lengths 64 and 66. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018; 5(3): 143-151. Vancouver Anev D , Harada M , Yankov N . New extremal singly even self-dual codes of lengths 64 and 66. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018; 5(3): 151-143.