论文标题
来自多扭曲代码的良好古典和量子代码
Good Classical and Quantum Codes from Multi-Twisted Codes
论文作者
论文摘要
引入了多键（MT）代码作为准倾斜（QT）代码的概括。已知QT代码包含许多良好的代码。在这项工作中，我们表明可以从MT代码获得具有良好参数和理想属性的代码。其中包括具有其他属性（例如可逆性和自以为是）的最佳和最佳经典代码，以及从特殊情况mt代码中获得的新的，最知名的非二进制量子代码。通常，文献中最知名的量子代码是通过考虑延伸环而间接获得的。我们的构造具有一个优势，即通过更直接，更简单的方法获得这些代码。此外，我们发现了关于有限领域的二项式的理论结果，这些结果在我们的搜索中很有用。
Multi-twisted (MT) codes were introduced as a generalization of quasi-twisted (QT) codes. QT codes have been known to contain many good codes. In this work, we show that codes with good parameters and desirable properties can be obtained from MT codes. These include best known and optimal classical codes with additional properties such as reversibility and self-duality, and new and best known non-binary quantum codes obtained from special cases MT codes. Often times best known quantum codes in the literature are obtained indirectly by considering extension rings. Our constructions have the advantage that we obtain these codes by more direct and simpler methods. Additionally, we found theoretical results about binomials over finite fields that are useful in our search.
