New extremal binary self-dual codes from F4 + uF4-lifts of quadratic double circulant codes over F4
Abstract
In this work, quadratic double and quadratic bordered double circulant constructions are applied to F4 + uF4 as well as F4, 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.
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