Symplectic QSD, LCD, and ACD Codes over a Non-Commutative Non-Unitary Ring of Order Nine

Key Points

• The study introduces quasi self-dual, linear complementary dual, and additive complementary dual codes.
• These codes are analyzed over a non-commutative non-unitary ring of order 9, establishing new connections.
• The characterization of right-symplectic ACD codes provides insights into their structural properties.
• Connections to symplectic–self-orthogonal and LCD ternary codes reinforce the relevance of these codes.