Let I be the commutative non-unital ring of order 4 defined by generators and relations.

Alahmadi et al. have classified QSD codes, Type IV codes (QSD codes with even weights) and quasi-Type IV codes (QSD codes with even torsion code) over I up to lengths \(n=6\), and suggested two building-up methods for constructing QSD codes. In this paper, we construct more QSD codes, Type IV codes and quasi-Type IV codes for lengths \(n=7\) and 8, and describe five new variants of the two building-up construction methods. We find that when \(n=8\) there is at least one QSD code with minimun distance 4, which attains the highest minimum distance so far, and we give a generator matrix for the code. We also describe some QSD codes, Type IV codes and quasi-Type IV codes with new weight distributions.

令I为由生成元和关系定义的 4 阶可交换非单位环。

阿拉赫马迪等人。已将 QSD 码、IV 型码（具有偶数权重的 QSD 码）和准 IV 型码（具有偶数扭转码的 QSD 码）分类到I长度为\(n=6\)，并建议了两种构建方法构建 QSD 代码。在本文中，我们构造了更多长度为\(n=7\)和8的QSD码、IV型码和准IV型码，并描述了这两种构建方法的五个新变体。我们发现当\(n=8\)时，至少有一个QSD 码的最小距离为4，它达到了迄今为​​止最大的最小距离，我们给出了该码的生成矩阵。我们还描述了一些具有新权重分布的 QSD 码、IV 型码和准 IV 型码。