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math.CO2025
New upper bounds for binary linear covering codes
Alexander A. Davydov, Stefano Marcugini, Fernanda Pambianco
The length function is the smallest length of a binary linear code with codimension (redundancy) and covering radius . We obtain the following new upper bounds…
math.CO2025
New infinite families of uniformly packed near-MDS codes and multiple coverings, based on the ternary Golay code
Alexander A. Davydov, Stefano Marcugini, Fernanda Pambianco
We present five new infinite families of linear near-MDS codes uniformly packed in the wide sense (UPWS). These codes are also almost perfect multiple coverings of the deep holes o…