Name
Abstract | ||
|---|---|---|
In analogy with the Singleton defect for classical codes, we propose a definition of rank defect for rank-metric codes. We characterize codes whose rank defect and dual rank defect are both zero, and prove that the rank distribution of such codes is determined by their parameters. This extends a result by Delsarte on the rank distribution of MRD codes. In the general case of codes of positive defect, we show that the rank distribution is determined by the parameters of the code, together with the number of codewords of small rank. Moreover, we prove that if the rank defect of a code and its dual are both one, and the dimension satisfies a divisibility condition, then the number of minimum-rank codewords and dual minimum-rank codewords is the same. Finally, we discuss how our results specialize to -linear rank-metric codes in vector representation. |
Year | DOI | Venue |
|---|---|---|
2018 | https://doi.org/10.1007/s10623-016-0325-1 | Des. Codes Cryptography |
Keywords | Field | DocType |
Rank-metric codes,Rank distribution,MRD,QMRD,and dually-QMRD codes,94B60,94C99,68P30 | Discrete mathematics,Combinatorics,Divisibility rule,Block code,Rank (graph theory),Linear code,Reed–Muller code,Rank of an abelian group,Weight distribution,Singleton,Mathematics | Journal |
Volume | Issue | ISSN |
86 | 1 | 0925-1022 |
Citations | PageRank | References |
5 | 0.46 | 1 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Javier de la Cruz | 1 | 9 | 2.28 |
| Elisa Gorla | 2 | 40 | 7.98 |
| Hiram H. López | 3 | 20 | 4.81 |
| Alberto Ravagnani | 4 | 32 | 9.46 |