Rank weight hierarchy of some classes of polynomial codes
We study the rank weight hierarchy, thus in particular the minimum rank distance, of polynomial codes over the finite field $\FF_{q^m}$, $q$ a prime power, $m \geq 2$. We assume that polynomials involved are squarefree. We establish the rank weight hierarchy of $[n,n-1]$ constacyclic codes. We chara...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/163959 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | We study the rank weight hierarchy, thus in particular the minimum rank distance, of polynomial codes over the finite field $\FF_{q^m}$, $q$ a prime power, $m \geq 2$. We assume that polynomials involved are squarefree. We establish the rank weight hierarchy of $[n,n-1]$ constacyclic codes. We characterize polynomial codes of $r$th rank weight $r$, and in particular of irst rank or minimum rank distance 1. Finally, we provide a refinement of the Singleton bound, from which we show that cyclic codes cannot be MRD (maximum rank distance) codes, but constacyclic codes can be. |
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