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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