TY - JOUR
T1 - Bordered constructions of self-dual codes from group rings and new extremal binary self-dual codes
AU - Dougherty, Steven T.
AU - Gildea, Joseph
AU - Korban, Adrian
AU - Kaya, Abidin
AU - Tylyshchak, Alexander
AU - Yildiz, Bahattin
N1 - Publisher Copyright:
© 2019
PY - 2019/5
Y1 - 2019/5
N2 - We introduce a bordered construction over group rings for self-dual codes. We apply the constructions over the binary field and the ring F 2 +uF 2 , using groups of orders 9, 15, 21, 25, 27, 33 and 35 to find extremal binary self-dual codes of lengths 20, 32, 40, 44, 52, 56, 64, 68, 88 and best known binary self-dual codes of length 72. In particular we obtain 41 new binary extremal self-dual codes of length 68 from groups of orders 15 and 33 using neighboring and extensions. All the numerical results are tabulated throughout the paper.
AB - We introduce a bordered construction over group rings for self-dual codes. We apply the constructions over the binary field and the ring F 2 +uF 2 , using groups of orders 9, 15, 21, 25, 27, 33 and 35 to find extremal binary self-dual codes of lengths 20, 32, 40, 44, 52, 56, 64, 68, 88 and best known binary self-dual codes of length 72. In particular we obtain 41 new binary extremal self-dual codes of length 68 from groups of orders 15 and 33 using neighboring and extensions. All the numerical results are tabulated throughout the paper.
KW - Bordered constructions
KW - Codes over rings
KW - Extremal codes
KW - Group rings
KW - Self-dual codes
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U2 - 10.1016/j.ffa.2019.02.004
DO - 10.1016/j.ffa.2019.02.004
M3 - Article
AN - SCOPUS:85061824264
SN - 1071-5797
VL - 57
SP - 108
EP - 127
JO - Finite Fields and Their Applications
JF - Finite Fields and Their Applications
ER -