Quasi type IV codes over a non-unital ring (Q2043852)

The authors introduce codes over a local ring of order \(4\) without identity. Following the notation for codes over \(\mathbb{F}_4\), they call the constructed codes quasi type IV codes. The authors give the general forms of generator matrices (Theorem 1) and parity check matrices (Theorem 2). Further, a construction of QSD codes is given, which the authors call multilevel construction (Theorem 4). In Section 5 of the paper, mass formulas for the constructed QSD codes are proven. Finally, in Section 6, the authors give a short length classification of the introduced codes for \(n\leq 3.\)