New extremal binary self-dual codes of length 68 from quadratic residue codes over F2 + uF2 + u2F2

Abstract

In this work, quadratic residue codes over the ring F-2 + uF(2) + u(2)F(2) with u(3) = u are considered. A duality and distance preserving Gray map from F-2+uF(2)+u(2)F(2) to F-2(3) in 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. (C) 2014 Elsevier Inc. All rights reserved.