Submodule codes as spherical codes in buildings

Abstract

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.