In this paper, we introduce a construction of quantum convolutional codes (QCCs) based on difference triangle sets (DTSs). To construct QCCs, one must determine polynomial stabilizers $X(D)$ and $Z(D)$ that commute (symplectic orthogonality), while keeping the stabilizers sparse and encoding memory small. To construct Z(D), we show that one can use a reflection of the DTS indices of X(D), where X(D) corresponds to a classical convolutional self-orthogonal code (CSOC) constructed from strong DTS supports. The motivation of this approach is to provide a constructive design that guarantees a prescribed minimum distance. We provide numerical results demonstrating the construction for a variety of code rates.

翻译：本文提出一种基于差分三角集（DTS）的量子卷积码（QCC）构造方法。构造QCC需确定满足交换关系（辛正交性）的多项式稳定子$X(D)$与$Z(D)$，同时保持稳定子稀疏性并控制编码记忆长度。为构造Z(D)，我们证明可通过反射X(D)的DTS索引实现，其中X(D)对应于由强DTS支撑构造的经典卷积自正交码（CSOC）。此方法的动机在于提供能保证预设最小距离的构造性设计方案。我们通过数值结果展示了多种码率下的构造实例。