Duadic Codes over Finite Commutative Rings

Abstract

Duadic codes are a generalization of quadratic residue codes. We obtain in this thesis quadratic residue codes over the chain ring F3+uF3; u2 = 0 and then obtain duadic codes for this ring. Also, we give a construction of duadic codes over the rings Z4 and F2+uF2; u2 = 0: We give specific constructions of these codes over finite fields and extend this construction to finite commutative chain rings Fq + uFq + u2Fq + ::: + us-1Fq with us = 0 where q = pr; p is a prime number and r ∈ Z.