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A geometric approach to generalized covering radii of linear codes
Gianira N. Alfarano, Giuseppe Marino, Alessandro Neri +1
Covering problems in coding theory are closely related to finite geometry through the interpretation of the columns of parity-check matrices as point sets in finite vector spaces.…
A lower bound on the minimum weight of some geometric codes
Bence Csajbók, Giovanni Longobardi, Giuseppe Marino +1
The -ary code associated with the incidence structure of points and -spaces in a projective space , where , is the -subspace generated…
A geometric characterization of known maximum scattered linear sets of
Giovanni Giuseppe Grimaldi, Somi Gupta, Giovanni Longobardi +1
An - linear set of is a set of points defined by non-zero vectors of an -subspac…
Evasive subspaces, generalized rank weights and near MRD codes
Giuseppe Marino, Alessandro Neri, Rocco Trombetti
We revisit and extend the connections between -linear rank-metric codes and evasive -subspaces of . We give a unifying framework…
A large family of maximum scattered linear sets of and their associated MRD codes
Giovanni Longobardi, Giuseppe Marino, Rocco Trombetti +1
The concept of linear set in projective spaces over finite fields was introduced by Lunardon in 1999 and it plays central roles in the study of blocking sets, semifields, rank-dist…
Evasive subspaces
Daniele Bartoli, Bence Csajbók, Giuseppe Marino +1
Let denote an -dimensional vector space over , the finite field of elements. Then is also an -dimension vector space over . An…