Abstract
<title>Abstract</title> <p>The development of quantum codes and entanglement-assisted quantum codes with improved parameters through classical codes has been a critical area in both quantum communications and quantum information theory. In this paper, we introduce a novel approach using a family of one-generator quasi-twisted codes of index 3 and provide an extended version of them that maintain self-orthogonality, enabling the creation of stabilizer quantum codes. Computational findings include the construction of binary stabilizer codes with good parameters. Additionally, we propose techniques to design maximal-entanglement entanglement-assisted quantum codes based on this class of quasi-twisted codes. As a practical outcome, we find some optimal quantum codes and good maximal-entanglement entanglement-assisted quantum codes derived from these class of quasi-twisted codes and their extension.</p>