Good Linear Codes from Quadratic Residue Codes over a Finite Non-Chain Ring

This paper is devoted to the study of quadratics residue codes and their extended codes over a finite non-chain ring. A class of Gray maps preserving the self-duality from the ring to the finite field are introduced. Some structural properties of quadratic residue codes and their extended codes are given. As an interesting applica-tion of these families of codes, some good linear codes are obtained by a special Gray map.