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math.CO2024
Binary codes from subset inclusion matrices
Alexey D. Marin, Ivan Yu. Mogilnykh
In this paper, we study the minimum distances of binary linear codes with parity check matrices formed from subset inclusion matrices , representing -element subsets…
math.CO2024
Completely regular codes with covering radius 1 and the second eigenvalue in 3-dimensional Hamming graphs
Ivan Mogilnykh, Anna Taranenko, Konstantin Vorob'ev
We obtain a classification of the completely regular codes with covering radius 1 and the second eigenvalue in the Hamming graphs H(3,q) up to q and intersection array. Due to work…