论文标题
f_ {q^2}的conjucyclic代码的代数结构
The algebraic structure of conjucyclic codes over F_{q^2}
论文作者
论文摘要
共济式代码是经典误差校正代码的重要且特殊的家族，该代码已用于构建二进制量子误差校正代码（QECC）。但是，目前，关于共珠法码的研究非常不足。本文将首次在$ \ mathbb {f} _ {q^{2}} $上探索添加剂conjucyclic代码的代数结构。主要通过$ \ mathbb {f} _ {q^{2}} $ down $ \ mathbb {f} _ {q} $的跟踪函数，我们首先将在$ q^2 $ -ary添加剂conjucyclic代码和$ q $ q $ - $ q $ -ary linear linear linear linear cyclic coces之间构建同构映射。由于映射保留了重量和正交性，因此将描述这些代码相对于交替的内部产品的双重结构。然后可以获得来自conjucyclic代码的QECC的新结构。最后，将确定$ q^2 $ - ARY添加剂conjucyclic代码的长度$ n $以及其发电机和奇偶校验检查矩阵的明确形式。
Conjucyclic codes are an important and special family of classical error-correcting codes, which have been used to construct binary quantum error-correcting codes (QECCs). However, at present, the research on the conjucyclic codes is extremely insufficient. This paper will explore the algebraic structure of additive conjucyclic codes over $\mathbb{F}_{q^{2}}$ for the first time. Mainly via the trace function from $\mathbb{F}_{q^{2}}$ down $\mathbb{F}_{q}$, we will firstly build an isomorphic mapping between $q^2$-ary additive conjucyclic codes and $q$-ary linear cyclic codes. Since the mapping preserves the weight and orthogonality, then the dual structure of these codes with respect to the alternating inner product will be described. Then a new construction of QECCs from conjucyclic codes can be obtained. Finally, the enumeration of $q^2$-ary additive conjucyclic codes of length $n$ and the explicit forms of their generator and parity-check matrices will be determined.
