Srikanth Pai, B. ; Sundar Rajan, B. (2015) On the bounds of certain maximal linear codes in a projective space IEEE Transactions on Information Theory, 61 (9). pp. 4923-4927. ISSN 0018-9448
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Official URL: http://ieeexplore.ieee.org/document/7132751/
Related URL: http://dx.doi.org/10.1109/TIT.2015.2449308
Abstract
The set of all subspaces of Fqn is denoted by Pq(n). The subspace distance dS(X, Y) = dim(X) + dim(Y) - 2 dim(X ∩ Y) defined on Pq(n) turns it into a natural coding space for error correction in random network coding. A subset of Pq(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 Pq(n). Braun et al. conjectured that the largest cardinality of a linear code, that contains Fqn, is 2n. In this paper, we prove this conjecture and characterize the maximal linear codes that contain Fqn.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Institute of Electrical and Electronics Engineers. |
| Keywords: | Random Network Coding; Linear Codes; Projective Spaces |
| ID Code: | 107808 |
| Deposited On: | 08 Dec 2017 10:13 |
| Last Modified: | 08 Dec 2017 10:13 |
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