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On the Bounds of Certain Maximal Linear Codes in a Projective Space.
- Source :
-
IEEE Transactions on Information Theory . Sep2015, Vol. 61 Issue 9, p4923-4927. 5p. - Publication Year :
- 2015
-
Abstract
- The set of all subspaces of \mathbb Fq^{n} is denoted by \mathbb Pq(n) . The subspace distance dS(X,Y) = \dim (X)+ \dim (Y)\, - 2\dim (X \cap Y) defined on \mathbb Pq(n) turns it into a natural coding space for error correction in random network coding. A subset of \mathbb P\vphantom {RRRq}(n) is called a code and the subspaces that belong to the code are called codewords. Motivated by classical coding theory, a linear coding structure can be imposed on a subset of \mathbb Pq(n) . Braun et al. conjectured that the largest cardinality of a linear code, that contains \mathbb Fq^{n} , is 2^n . In this paper, we prove this conjecture and characterize the maximal linear codes that contain \mathbb Fq^{n} . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 61
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 108970781
- Full Text :
- https://doi.org/10.1109/TIT.2015.2449308