Large constant dimension codes and lexicodes

Pages: 177 - 189, Volume 5, Issue 2, May 2011

doi:10.3934/amc.2011.5.177       Abstract        References        Full Text (349.6K)       Related Articles

Natalia Silberstein - Computer Science Department, Technion - Israel Institute of Technology, Haifa, 32000, Israel (email)
Tuvi Etzion - Computer Science Department, Technion - Israel Institute of Technology, Haifa, 32000, Israel (email)

Abstract: Constant dimension codes, with a prescribed minimum distance, have found recently an application in network coding. All the codewords in such a code are subspaces of $\mathbb F$_qⁿ with a given dimension. A computer search for large constant dimension codes is usually inefficient since the search space domain is extremely large. Even so, we found that some constant dimension lexicodes are larger than other known codes. We show how to make the computer search more efficient. In this context we present a formula for the computation of the distance between two subspaces, not necessarily of the same dimension.

Keywords:  Grassmannian, constant dimension code, lexicode, Ferrers diagram.
Mathematics Subject Classification:  Primary: 14M15, 94B60; Secondary: 94B65.

Received: March 2010;      Revised: September 2010;      Published: May 2011.

 References