By exploiting the connection between scattered Fq-subspaces of F3q m and minimal nondegenerate 3-dimensional rank-metric codes of Fnq m, n ≥q m + 2, described in [G. N. Alfarano et al., J. Combin. Theory Ser. A, 192 (2022), 105658], we will exhibit a new class of codes with parameters [m+ 2, 3,m 2]qm/q for infinite values of q and m ≥q 5 odd. Moreover, by studying the geometric structures of these scattered subspaces, we determine the rank weight distribution of the associated codes.
SHORT RANK-METRIC CODES AND SCATTERED SUBSPACES / Lia, S.; Longobardi, G.; Marino, G.; Trombetti, R.. - In: SIAM JOURNAL ON DISCRETE MATHEMATICS. - ISSN 0895-4801. - 38:4(2024), pp. 2578-2598. [10.1137/23M1574749]
SHORT RANK-METRIC CODES AND SCATTERED SUBSPACES
Longobardi G.;Marino G.
;Trombetti R.
2024
Abstract
By exploiting the connection between scattered Fq-subspaces of F3q m and minimal nondegenerate 3-dimensional rank-metric codes of Fnq m, n ≥q m + 2, described in [G. N. Alfarano et al., J. Combin. Theory Ser. A, 192 (2022), 105658], we will exhibit a new class of codes with parameters [m+ 2, 3,m 2]qm/q for infinite values of q and m ≥q 5 odd. Moreover, by studying the geometric structures of these scattered subspaces, we determine the rank weight distribution of the associated codes.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
