On the generalised rank weights of quasi-cyclic codes
Generalised rank weights were formulated in analogy to Wei's generalised Hamming weights, but for the rank metric. In this paper we study the generalised rank weights of quasi-cyclic codes, a special class of linear codes usually studied for their properties in error correction over the Hamming...
Saved in:
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/154932 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | Generalised rank weights were formulated in analogy to Wei's generalised Hamming weights, but for the rank metric. In this paper we study the generalised rank weights of quasi-cyclic codes, a special class of linear codes usually studied for their properties in error correction over the Hamming metric. By using the algebraic structure of quasi-cyclic codes, a new upper bound on the generalised rank weights of quasi-cyclic codes is formulated, which is tighter than the known Singleton bound. Additionally, it is shown that the first generalised rank weight of self-dual $1$-generator quasi-cyclic codes is almost completely determined by the choice of $F_{q^m}$. |
|---|