Abstract Let I be a homogeneous ideal in polynomial ring S . In this paper, we extend the study of asymptotic behavior minimum distance function δ and give bounds for its stabilization point, r , when is an F -pure or square-free monomial ideal. These are related with dimension Castelnuovo–Mumford regularity

Dihedral codes, particular cases of quasi-cyclic have a nice algebraic structure which allows to store them efficiently. In this paper, we investigate it and prove some lower bounds on their dimension minimum distance, in analogy with the theory BCH codes. This us construct dihedral codes prescribed distance. binary case, present examples optimal obtained by construction.