New extremal binary self-dual codes from a modified four circulant construction

In this work, we propose a modified four circulant construction for self-dual codes and a bordered version of the construction using the properties of lambda-circulant and lambda-reverse circulant matrices. By using the constructions on F-2, we obtain new binary codes of lengths 64 and 68. We also apply the constructions to the ring R-2 and considering the F2 and R-1-extensions, we obtain new singly-even extremal binary self-dual codes of lengths 66 and 68. More precisely, we find 3 new codes of length 64, 13 new codes of length 66 and 21 new codes of length 68. These codes all have weight enumerators with parameters that were not known to exist in the literature. (C) 2015 Elsevier B.V. All rights reserved.