TY  - JOUR
T1  - New extremal binary self-dual codes of length 68
TT  - New extremal binary self-dual codes of length 68
AU  - Kaya, Abidin
AU  - Yildiz, Bahattin
PY  - 2014
DA  - March
DO  - 10.13069/jacodesmath.79879
JF  - Journal of Algebra Combinatorics Discrete Structures and Applications
PB  - iPeak Academy
WT  - DergiPark
SN  - 2148-838X
SP  - 29
EP  - 39
VL  - 1
IS  - 1
LA  - en
AB  - In this correspondence, we consider quadratic double and bordered double circulant construction methods over the ring R := F_2 + uF_2 + u^2F_2, where u^3 = 1. Among other examples, extremal binary self-dual codes of length 66 are obtained by these constructions. These are extended by using extension theorems for self-dual codes and as a result 8 new extremal binary self-dual codes of length 68 are obtained. More precisely, codes with beta=117, 120, 133 in W68;1 and with gamma = 1, beta=49, 57, 59 and codes with gamma=2, beta=69, 81 in W68;2 are constructed for the ?first time in the literature. In addition to these, some known such codes are reconstructed via this extension. The results are tabulated.
KW  - Extremal codes
KW  - Codes over rings
KW  - Gray maps
KW  - Quadratic double-circulant codes
N2  - In this correspondence, we consider quadratic double and bordered double circulant construction methods over the ring R := F_2 + uF_2 + u^2F_2, where u^3 = 1. Among other examples, extremal binary self-dual codes of length 66 are obtained by these constructions. These are extended by using extension theorems for self-dual codes and as a result 8 new extremal binary self-dual codes of length 68 are obtained. More precisely, codes with beta=117, 120, 133 in W68;1 and with gamma = 1, beta=49, 57, 59 and codes with gamma=2, beta=69, 81 in W68;2 are constructed for the ?first time in the literature. In addition to these, some known such codes are reconstructed via this extension. The results are tabulated.
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UR  - https://doi.org/10.13069/jacodesmath.79879
L1  - https://dergipark.org.tr/en/download/article-file/148544
ER  -