论文标题
一致的标志代码
Consistent Flag Codes
论文作者
论文摘要
在本文中，我们在$ \ mathbb {f} _q^n $上研究标志代码，为$ \ mathbb {f} _q $带有$ q $元素的有限字段。特别注意标志代码的参数和属性之间的连接以及与之自然相关的恒定维度代码的家族的连接（投影代码）。更确切地说，我们专注于一致的标志代码，即，距离和大小的标志代码完全由其投影代码确定。我们通过将等距和向日葵子空间代码的概念推广到标志代码设置的概念来探讨该代码家族的某些方面，并介绍它们的示例。最后，我们提出了一种完全利用一致性条件的一致标志代码的解码算法。
In this paper we study flag codes on $\mathbb{F}_q^n$, being $\mathbb{F}_q$ the finite field with $q$ elements. Special attention is given to the connection between the parameters and properties of a flag code and the ones of a family of constant dimension codes naturally associated to it (the projected codes). More precisely, we focus on consistent flag codes, that is, flag codes whose distance and size are completely determined by their projected codes. We explore some aspects of this family of codes and present examples of them by generalizing the concepts of equidistant and sunflower subspace code to the flag codes setting. Finally, we present a decoding algorithm for consistent flag codes that fully exploits the consistency condition.
