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Bounds on Subspace Codes Based on Orthogonal Space Over Finite Fields of Characteristic 2.
- Source :
-
International Journal of Foundations of Computer Science . Aug2019, Vol. 30 Issue 5, p735-757. 23p. - Publication Year :
- 2019
-
Abstract
- In this paper, the Sphere-packing bound, Wang-Xing-Safavi-Naini bound, Johnson bound and Gilbert-Varshamov bound on the subspace code of length 2 ν + δ , size M , minimum subspace distance 2 j based on m -dimensional totally singular subspace in the (2 ν + δ) -dimensional orthogonal space 𝔽 q (2 ν + δ) over finite fields 𝔽 q of characteristic 2, denoted by (2 ν + δ , M , 2 j , m) q , are presented, where ν is a positive integer, δ = 0 , 1 , 2 , 0 ≤ m ≤ ν , 0 ≤ j ≤ m. Then, we prove that (2 ν + δ , M , 2 j , m) q codes attain the Wang-Xing-Safavi-Naini bound if and only if they are certain Steiner structures in ℳ (m , 0 , 0 ; 2 ν + δ) , where ℳ (m , 0 , 0 ; 2 ν + δ) denotes the collection of all the m -dimensional totally singular subspaces in the (2 ν + δ) -dimensional orthogonal space 𝔽 q (2 ν + δ) over 𝔽 q of characteristic 2. Finally, Gilbert-Varshamov bound and linear programming bound on the subspace code (2 ν + δ , M , d) q in ℳ (2 ν + δ) are provided, where ℳ (2 ν + δ) denotes the collection of all the totally singular subspaces in the (2 ν + δ) -dimensional orthogonal space 𝔽 q (2 ν + δ) over 𝔽 q of characteristic 2. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01290541
- Volume :
- 30
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- International Journal of Foundations of Computer Science
- Publication Type :
- Academic Journal
- Accession number :
- 138033634
- Full Text :
- https://doi.org/10.1142/S0129054119500199