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：我们通过有限交换链环上的模码给出了子空间码的一种推广。我们定义了一类新的斯佩纳码，并利用极值组合学的结果证明了此类码在不同情形下的最优性。此外，我们阐释了其与布鲁哈-蒂茨建筑的关联，并展示了我们的码如何成为欧几里得意义下球面码在该建筑中的类似物。