New extremal binary self-dual codes from F_4 + uF_4-lifts of quadratic   double circulant codes over F_4
  In this work, quadratic double and quadratic bordered double circulant constructions are applied to F_4 + uF_4 as well as F_4, as a result of which extremal binary self-dual codes of length 56 and 64 are obtained. The binary extension theorems as well as the ring extension version are used to obtain 7 extremal self-dual binary codes of length 58, 24 extremal self-dual binary codes of length 66 and 29 extremal self-dual binary codes of length 68, all with new weight enumerators, updating the list of all the known extremal self-dual codes in the literature. 
Abidin Kaya, Bahattin Yildiz, and Irfan Siap
math.CO cs.IT math.IT