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Submodule codes as spherical codes in buildings
Published 27 Feb 2022 in cs.IT, math.CO, and math.IT | (2202.13370v3)
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.
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