We give a generalization of subspace codes by means of codes of modules over finite commutative chain rings. We define a new class of Sperner codes and use results from extremal combinatorics to prove the optimality of such codes in different cases. Moreover, we explain the connection with Bruhat-Tits buildings and show how our codes are the buildings' analogue of spherical codes in the Euclidean sense.
翻译:我们通过对有限通量链环的模块编码,对亚空间代码进行概括化。我们定义了一个新的Sperner代码类别,并使用极端组合式代码的结果,以证明这些代码在不同情况下的最佳性。此外,我们解释了与布鲁哈特-提茨建筑的联系,并展示了我们的代码是如何在欧几里德意义上模拟这些建筑的球代码的。</s>