SHORT RANK-METRIC CODES AND SCATTERED SUBSPACES

被引：0

作者：

Lia, Stefano ^{[1
]}

Longobardi, Giovanni

Marino, Giuseppe ^{[2
]}

Trombetti, Rocco ^{[2
]}

机构：

[1] Univ Coll Dublin, Sch Math & Stat, Dublin, Ireland

[2] Univ Naples Federico II, Dept Math & Applicat Renato Caccioppoli, Via Cintia, I-80126 Naples, Italy

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2024年 / 38卷 / 04期

关键词：

scattered subspaces; linear sets; cutting blocking sets; rank-metric codes; POLYNOMIALS; FIELD;

D O I：

10.1137/23M1574749

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By exploiting the connection between scattered F-q-subspaces of F-qm(3) and minimal nondegenerate 3-dimensional rank-metric codes of F-qm(n), n >= 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 >= 5 odd. Moreover, by studying the geometric structures of these scattered subspaces, we determine the rank weight distribution of the associated codes.

引用

页码：2578 / 2598

页数：21

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