On quasi-cyclic subspace codes

TL;DR

This paper generalizes cyclic subspace codes to m-quasi cyclic codes, extending existing construction methods like subspace polynomials and Frobenius mappings for better network coding solutions.

Contribution

It introduces m-quasi cyclic subspace codes and adapts traditional cyclic code construction techniques to this new class.

Findings

m-quasi cyclic codes generalize cyclic codes

Construction methods like subspace polynomials apply to m-quasi cyclic codes

Potential for improved network coding performance

Abstract

Construction of subspace codes with good parameters is one of the most important problems in random network coding. In this paper we present first a generalization of the concept of cyclic subspaces codes and further we show that the usual methods for constructing cyclic subspace codes over finite fields works for m-quasi cyclic codes, namely the subspaces polynomials and Frobenius mappings.