Projective Space Codes for the Injection Metric

Abstract

In the context of error control in random linear network coding, it is useful to construct codes that comprise well-separated collections of subspaces of a vector space over a finite field. In this paper, the metric used is the so-called "injection distance", introduced by Silva and Kschischang. A Gilbert-Varshamov bound for such codes is derived. Using the code-construction framework of Etzion and Silberstein, new non-constant-dimension codes are constructed; these codes contain more codewords than comparable codes designed for the subspace metric.