# American Institute of Mathematical Sciences

February  2016, 10(1): 113-130. doi: 10.3934/amc.2016.10.113

## On applications of orbit codes to storage

 1 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore

Received  December 2014 Revised  July 2015 Published  March 2016

We consider orbit codes, namely subspace codes obtained from orbits of the action of subgroups of $GL_n(\mathbb{F}_q)$ on $m$-dimensional subspaces of $\mathbb{F}_q^n$. We discuss their applicability to design storage codes, in particular in the context of collaborative repair: we identify known storage codes that can be interpreted as orbit codes, motivate why orbit codes provide good candidates for storage codes, and translate the storage code parameters into those of the algebraic objects involved. Two simple families of storage orbit codes are given.
Citation: Shiqiu Liu, Frédérique Oggier. On applications of orbit codes to storage. Advances in Mathematics of Communications, 2016, 10 (1) : 113-130. doi: 10.3934/amc.2016.10.113
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