New extremal binary self-dual codes of length 68 from quadratic residue codes over ^{F 2} + u^{F 2} + ^{u 2F 2}

In this work, quadratic residue codes over the ring ^F2+u ^F2+^u2F2 with ^u3=u are considered. A duality and distance preserving Gray map from ^F2+u^F2+ ^u2F2 to F23 is defined. By using quadratic double circulant, quadratic bordered double circulant constructions and their extensions self-dual codes of different lengths are obtained. As Gray images of these codes and their extensions, a substantial number of new extremal self-dual binary codes are found. More precisely, thirty two new extremal binary self-dual codes of length 68, 363 Type I codes of parameters [72,36,12], a Type II [72,36,12] code and a Type II [96,48,16] code with new weight enumerators are obtained through these constructions. The results are tabulated.