Constructing formally self-dual codes from block λ-circulant matrices

In this work, construction methods for formally self-dual codes are generalized in the form of block λ-circulant matrices. The constructions are applied over the rings F₂, R₁ = F₂ + uF₂ and S = F₂[u]/(u³ − 1). Using n-block λ-circulant matrices for suitable integers n and units λ, many binary FSD codes (as Gray images) with a higher minimum distance than best known self-dual codes of lengths 34, 40, 44, 54, 58, 70, 72 and 74 were obtained. In particular, ten new even FSD [72,36,14] codes were constructed together with eight new near-extremal FSD even codes of length 44 and twenty-five new near-extremal FSD even codes of length 36.