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 TRANSACTIONS ON INFORMATION THEORY, 61 (9). pp. 4923-4927.

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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)-2dim(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 et al. 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:	Journal Article
Publication:	IEEE TRANSACTIONS ON INFORMATION THEORY
Publisher:	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Additional Information:	Copy right for this article belongs to the IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 445 HOES LANE, PISCATAWAY, NJ 08855-4141 USA
Keywords:	Linear codes; projective spaces; random network coding
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	24 Sep 2015 04:47
Last Modified:	24 Sep 2015 04:47
URI:	http://eprints.iisc.ac.in/id/eprint/52388

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