New extremal binary self-dual codes from F4+uF4F4+uF4-lifts of quadratic circulant codes over F4F4

In this work, quadratic double and quadratic bordered double circulant constructions are applied to F4+uF4F4+uF4 as well as to F4F4, and as a result, 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 seven extremal self-dual binary codes of length 58, twenty-four extremal self-dual binary codes of length 66 and twenty-nine 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.