Dihedral Group Codes Over Finite Fields
Yun Fan, Liren Lin
Abstract
Bazzi and Mitter showed that binary dihedral group codes are asymptotically good. In this paper we prove that the dihedral group codes over any finite field with strong duality property are asymptotically good. If the characteristic of the field is even, self-dual dihedral group codes are asymptotically good. If the characteristic of the field is odd, maximal self-orthogonal dihedral group codes and LCD dihedral group codes are asymptotically good.
Topics & Concepts
Dihedral groupMathematicsDihedral angleGroup (periodic table)Duality (order theory)Discrete mathematicsCombinatoricsPure mathematicsPhysicsHydrogen bondMoleculeQuantum mechanicsCoding theory and cryptographyCooperative Communication and Network CodingError Correcting Code Techniques