Submodule codes as spherical codes in buildings
Information Theory
2023-09-25 v3 Combinatorics
math.IT
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.
Keywords
Cite
@article{arxiv.2202.13370,
title = {Submodule codes as spherical codes in buildings},
author = {Mima Stanojkovski},
journal= {arXiv preprint arXiv:2202.13370},
year = {2023}
}
Comments
21 pages, revision including the referees' suggestions, to appear in Designs, Codes and Cryptography