In network coding, a flag code is a collection of flags, that is, sequences of nested subspaces of a vector space over a finite field. Due to its definition as the sum of the corresponding subspace distances, the flag distance parameter encloses a hidden combinatorial structure. To bring it to light, in this paper, we interpret flag distances by means of distance paths drawn in a convenient distance support. The shape of such a support allows us to create an ad hoc associated Ferrers diagram frame where we develop a combinatorial approach to flag codes by relating the possible realizations of their minimum distance to different partitions of appropriate integers. This novel viewpoint permits to establish noteworthy connections between the flag code parameters and the ones of its projected codes in terms of well known concepts coming from the classical partitions theory.
翻译：在网络编码中,国旗代码是一组国旗,即矢量空间在一定字段上的嵌套子空间序列。由于旗帜距离参数的定义是相应的子空间距离的总和,因此,旗帜距离参数包含隐藏的组合结构。为了让大家看到这一点,我们在本文件中通过在方便的距离支持下绘制的距离路径来解释旗帜距离。这种支持的形状使我们能够创建一个与Ferres相联的特设图表框架,通过将可能实现的最短距离与适当的整数的不同分区联系起来,对旗帜代码制定组合式方法。这个新观点允许在国旗代码参数与其预测的代码参数之间建立值得注意的联系,其根据古典分区理论中众所周知的概念。
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