Constant-Rank Codes and Their Connection to Constant-Dimension Codes - Computer Science > Information TheoryReport as inadecuate




Constant-Rank Codes and Their Connection to Constant-Dimension Codes - Computer Science > Information Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: Constant-dimension codes have recently received attention due to theirsignificance to error control in noncoherent random linear network coding. Whatthe maximal cardinality of any constant-dimension code with finite dimensionand minimum distance is and how to construct the optimal constant-dimensioncode or codes that achieves the maximal cardinality both remain open researchproblems. In this paper, we introduce a new approach to solving these twoproblems. We first establish a connection between constant-rank codes andconstant-dimension codes. Via this connection, we show that optimalconstant-dimension codes correspond to optimal constant-rank codes overmatrices with sufficiently many rows. As such, the two aforementioned problemsare equivalent to determining the maximum cardinality of constant-rank codesand to constructing optimal constant-rank codes, respectively. To this end, wethen derive bounds on the maximum cardinality of a constant-rank code with agiven minimum rank distance, propose explicit constructions of optimal orasymptotically optimal constant-rank codes, and establish asymptotic bounds onthe maximum rate of a constant-rank code.



Author: Maximilien Gadouleau, Zhiyuan Yan

Source: https://arxiv.org/







Related documents