Galois Cyclic 通用轨道旗帜编码 (On Generalized Galois Cyclic Orbit Flag Codes)

Flag codes that are orbits of a cyclic subgroup of the general linear group acting on flags of a vector space over a finite field, are called cyclic orbit flag codes. In this paper we present a new contribution to the study of such codes started in arXiv:2102.00867, by focusing this time on the generating flag. More precisely, we examine those ones whose generating flag has at least one subfield among its subspaces. In this situation, two important families arise: the already known Galois flag codes, in case we have just fields, or the generalized Galois flag codes in other case. We investigate the parameters and properties of the latter ones and explore the relationship with their underlying Galois flag code.

翻译：普通线性组在有限场内悬挂矢量空间旗帜的一般线性分组的圆形分组的轨道旗码称为环轨道旗码。在本文中,我们介绍了对此类编码研究的新贡献,该研究始于arXiv:2102.00867,这次侧重于生成的旗帜。更准确地说,我们研究那些其生成的旗帜在其子空间中至少有一个子领域。在这种情况下,产生了两个重要组别:已知的加洛瓦旗码,如果我们只有字段,或通用加洛瓦旗码。我们调查了后者的参数和特性,并探索了这些参数和特性与伽洛瓦旗根本代码之间的关系。