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 application of these families of codes, some good linear codes are obtained by a special Gray map.