On the Bounds of Certain Maximal Linear Codes in a Projective Space

Pai, Srikanth B and Rajan, Sundar B (2015) On the Bounds of Certain Maximal Linear Codes in a Projective Space. In: IEEE International Symposium on Information Theory (ISIT, JUN 14-19, 2015, Hong Kong, PEOPLES R CHINA, pp. 591-595.

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Abstract

The set of all subspaces of F-q(n) is denoted by P-q(n). The subspace distance d(S)(X, Y) = dim (X) + dim (Y) - 2 dim (X boolean AND Y) defined on P-q(n) turns it into a natural coding space for error correction in random network coding. A subset of P-q(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 P-q(n). Braun, Etzion and Vardy conjectured that the largest cardinality of a linear code, that contains F-q(n), is 2(n). In this paper, we prove this conjecture and characterize the maximal linear codes that contain F-q(n).

Item Type:	Conference Paper
Series.:	IEEE International Symposium on Information Theory
Additional Information:	Copy right for this article belongs to the IEEE, 345 E 47TH ST, NEW YORK, NY 10017 USA
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	07 Dec 2016 05:28
Last Modified:	07 Dec 2016 05:28
URI:	http://eprints.iisc.ac.in/id/eprint/55506

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