Traian Muntean, Dimitrios Poulakis, Robert Rolland

Affiliations:

^{1} Department of Mathematics, Science and Technology, Aarhus University^{2} Department of Mathematics, Science and Technology, Aarhus University

DOI:

10.1007/978-3-642-40663-8_9

Abstract:

We present a general theory to obtain good linear network codes utilizing the osculating nature of algebraic varieties. In particular, we obtain from the osculating spaces of Veronese varieties explicit families of equidimensional vector spaces, in which any pair of distinct vector spaces intersects in the same dimension. Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possible altered vector space. Ralf Koetter and Frank R. Kschischang introduced a metric on the set af vector spaces and showed that a minimal distance decoder for this metric achieves correct decoding if the dimension of the intersection of the transmitted and received vector space is sufficiently large. The obtained osculating spaces of Veronese varieties are equidistant in the above metric. The parameters of the resulting linear network codes are determined.

ISBN:

9783642406638, 9783642406621

Type:

Conference paper

Language:

English

Published in:

Lecture Notes in Computer Science: 5th International Conference, Cai 2013, 2013, p. 83-88

Main Research Area:

Science/technology

Publication Status:

Published

Series:

Lecture Notes in Computer Science

Review type:

Peer Review

Conference:

5th International Conference on Algebraic Informatics, 2013