论文标题
两个经典传播规则及其应用的船体
The hull of two classical propagation rules and their applications
论文作者
论文摘要
在这项工作中，我们研究并确定了两个经典繁殖规则的欧几里得和赫尔米亚人船体的维度，即直接总和构造和$（\ mathbf {u}，\ m athbf {u+v}）$ - 构造。给出了从这两个传播规则得出的产生代码的一些新标准，它是自偶，自动或线性互补双（LCD）代码的一些新标准。作为一个应用程序，我们构建了一些具有规定的船体尺寸的线性代码，许多新的二进制，三元欧几里得正式形式上是自二（FSD）LCD代码和Quaternary Hermitian FSD LCD LCD代码。还获得了一些新的类似奇怪的，奇特的，欧几里得和遗传性自动守则。根据Markus GrassL维护的数据库，许多{这些}代码也（几乎）是最佳的。我们的方法对改善已知LCD代码的最小距离的下限产生了积极的贡献。
In this work, we study and determine the dimensions of Euclidean and Hermitian hulls of two classical propagation rules, namely, the direct sum construction and the $(\mathbf{u},\mathbf{u+v})$-construction. Some new criteria for the resulting codes derived from these two propagation rules being self-dual, self-orthogonal, or linear complementary dual (LCD) codes are given. As an application, we construct some linear codes with prescribed hull dimensions, many new binary, ternary Euclidean formally self-dual (FSD) LCD codes, and quaternary Hermitian FSD LCD codes. Some new even-like, odd-like, Euclidean and Hermitian self-orthogonal codes are also obtained. Many of {these} codes are also (almost) optimal according to the Database maintained by Markus Grassl. Our methods contribute positively to improve the lower bounds on the minimum distance of known LCD codes.
