Some results on quadratic residue codes over the ring Fp + vFp + v2Fp + v3Fp

Abstract

Quadratic residue (QR) codes and their extensions over the finite non-chain ring [Formula: see text] are studied, where [Formula: see text], [Formula: see text] is an odd prime and [Formula: see text]. A class of Gray maps preserving the self-duality of linear codes from [Formula: see text] to [Formula: see text] is given. Under a special Gray map, a self-dual code [Formula: see text] over [Formula: see text], a formally self-dual code [Formula: see text] over [Formula: see text] and a formally self-dual code [Formula: see text] over [Formula: see text] are obtained from extended QR codes.