Quadratic residue codes over ${\mathbb Z}_{49}$

In this paper, we investigate quadratic residue codes of prime length [Formula: see text] over [Formula: see text] where [Formula: see text] or [Formula: see text] These codes are defined via their generating idempotents, and we examine their extended versions. Furthermore, we demonstrate that the extended quadratic residue codes over [Formula: see text] possess large automorphism groups, a property that can be effectively exploited in decoding algorithms.