Let (Formula presented.) denote an (Formula presented.) -dimensional vector space over (Formula presented.), the finite field of (Formula presented.) elements. Then (Formula presented.) is also an (Formula presented.) -dimension vector space over (Formula presented.). An (Formula presented.) -subspace (Formula presented.) of (Formula presented.) is (Formula presented.) -evasive if it meets the (Formula presented.) -dimensional (Formula presented.) -subspaces of (Formula presented.) in (Formula presented.) -subspaces of dimension at most (Formula presented.). The (Formula presented.) -evasive subspaces are known as scattered and they have been intensively studied in finite geometry, their maximum size has been proved to be (Formula presented.) when (Formula presented.) is even or (Formula presented.). We investigate the maximum size of (Formula presented.) -evasive subspaces, study two duality relations among them and provide various constructions. In particular, we present the first examples, for infinitely many values of (Formula presented.), of maximum scattered subspaces when (Formula presented.) and (Formula presented.). We obtain these examples in characteristics 2, 3 and 5.
Evasive subspaces / Bartoli, D.; Csajbok, B.; Marino, G.; Trombetti, R.. - In: JOURNAL OF COMBINATORIAL DESIGNS. - ISSN 1063-8539. - 29:8(2021), pp. 533-551. [10.1002/jcd.21783]
Evasive subspaces
Marino G.;Trombetti R.
2021
Abstract
Let (Formula presented.) denote an (Formula presented.) -dimensional vector space over (Formula presented.), the finite field of (Formula presented.) elements. Then (Formula presented.) is also an (Formula presented.) -dimension vector space over (Formula presented.). An (Formula presented.) -subspace (Formula presented.) of (Formula presented.) is (Formula presented.) -evasive if it meets the (Formula presented.) -dimensional (Formula presented.) -subspaces of (Formula presented.) in (Formula presented.) -subspaces of dimension at most (Formula presented.). The (Formula presented.) -evasive subspaces are known as scattered and they have been intensively studied in finite geometry, their maximum size has been proved to be (Formula presented.) when (Formula presented.) is even or (Formula presented.). We investigate the maximum size of (Formula presented.) -evasive subspaces, study two duality relations among them and provide various constructions. In particular, we present the first examples, for infinitely many values of (Formula presented.), of maximum scattered subspaces when (Formula presented.) and (Formula presented.). We obtain these examples in characteristics 2, 3 and 5.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
