Submodule codes as spherical codes in buildings
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Submission date: 04. Mar. 2022
MSC-Numbers: 94B60, 94B65, 94B25, 20E42, 51E24, 52B20
Keywords and phrases: submodule codes, Sperner codes, spherical codes, Sperner property, Bruhat-Tits buildings
Link to arXiv: See the arXiv entry of this preprint.
In this paper, we give a generalization of subspace codes by means of codes of modules over finite commutative chain rings. We define the 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.