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

In this work, construction methods for formally self-dual codes are generalized in the form of block lambda-circulant matrices. The constructions are applied over the rings F_2,R1 = F_2 + uF_2 and S = F_2[u]=(u^3-1). Using n-block lambda-circulant matrices for suitable integers n and units lambda, 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 twentyfive new near-extremal FSD even codes of length 36

On self-dual double circulant codes

Self-dual double circulant codes of odd dimension are shown to be dihedral in even characteristic and consta-dihedral in odd characteristic. Exact counting formulae are derived for them and used to show they contain families of codes with relative distance satisfying a modified Gilbert-Varshamov bound.Comment: 8 page