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On maximum additive Hermitian rank-metric codes
- Publication Year :
- 2021
-
Abstract
- Inspired by the work of Zhou "On equivalence of maximum additive symmetric rank-distance codes" (2020) based on the paper of Schmidt "Symmetric bilinear forms over finite fields with applications to coding theory" (2015), we investigate the equivalence issue of maximum $d$-codes of Hermitian matrices. More precisely, in the space $\mathrm{H}_n(q^2)$ of Hermitian matrices over $\mathbb{F}_{q^2}$ we have two possible equivalence: the classical one coming from the maps that preserve the rank in $\mathbb{F}_{q^2}^{n\times n}$, and the one that comes from restricting to those maps preserving both the rank and the space $\mathrm{H}_n(q^2)$. We prove that when $d<br />Comment: Accepted for publication in Journal of Algebraic Combinatorics
- Subjects :
- Algebra and Number Theory
05E15, 05E30, 51E22
Rank (linear algebra)
010102 general mathematics
0102 computer and information sciences
Hermitian matrix
Space (mathematics)
01 natural sciences
Combinatorics
Hermitian matrix, Rank Metric code,Linearized polynomial
Linearized polynomial
010201 computation theory & mathematics
Metric (mathematics)
FOS: Mathematics
Mathematics - Combinatorics
Discrete Mathematics and Combinatorics
Equivalence relation
Combinatorics (math.CO)
0101 mathematics
Algebraic number
Rank metric code
Equivalence (measure theory)
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....1aa0fd93b02ca2bd844b0ee0871e0fec