Isometry and Automorphisms of Constant Dimension Codes

TL;DR

This paper explores the symmetries of constant dimension codes used in network coding by defining isometries and analyzing their automorphism groups, providing insights into their structural properties.

Contribution

It introduces definitions of linear and semilinear isometries for subspace codes and studies the automorphism groups of existing constant dimension code constructions.

Findings

Characterization of isometry classes of constant dimension codes

Results on automorphism groups of known code constructions

Insights into the structural symmetries of subspace codes

Abstract

We define linear and semilinear isometry for general subspace codes, used for random network coding. Furthermore, some results on isometry classes and automorphism groups of known constant dimension code constructions are derived.