Construction of isodual codes from polycirculant matrices

Double polycirculant codes are introduced here as a generalization of double circulant codes. When the matrix of the polyshift is a companion matrix of a trinomial, we show that such a code is isodual, hence formally self-dual. Numerical examples show that the codes constructed have optimal or quasi-optimal parameters amongst formally self-dual codes. Self-duality, the trivial case of isoduality, can only occur over \F_2 in the double circulant case. Building on an explicit infinite sequence of irreducible trinomials over \F_2, we show that binary double polycirculant codes are asymptotically good

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