New binary self-dual codes of lengths 56, 58, 64, 80 and 92 from a modification of the four circulant construction

In this work, we give a new technique for constructing self-dual codes over commutative Frobenius rings using $\lambda$-circulant matrices. The construction was derived as modification of the well-known four circulant codes. Applying together with building-up construction, construct singly-even binary lengths 56, 58, 64, 80 and 92 that were not known in literature before. Singly-even length $\beta\in\{2,4,5,6,8\}$ their weight enumerators are constructed first time literature.