Constructions of cyclic constant dimension codes

TL;DR

This paper investigates the construction of cyclic constant dimension codes, aiming to maximize code size and minimum distance, and extends previous methods to develop new code constructions for applications in network coding.

Contribution

It introduces new constructions of cyclic constant dimension codes and extends existing results from prior research to improve code parameters.

Findings

New cyclic constant dimension codes constructed.

Extended previous results to larger code parameters.

Enhanced encoding and decoding efficiency for network applications.

Abstract

Subspace codes and particularly constant dimension codes have attracted much attention in recent years due to their applications in random network coding. As a particular subclass of subspace codes, cyclic subspace codes have additional properties that can be applied efficiently in encoding and decoding algorithms. It is desirable to find cyclic constant dimension codes such that both the code sizes and the minimum distances are as large as possible. In this paper, we explore the ideas of constructing cyclic constant dimension codes proposed in \big([2], IEEE Trans. Inf. Theory, 2016\big) and \big([17], Des. Codes Cryptogr., 2016\big) to obtain further results. Consequently, new code constructions are provided and several previously known results in [2] and [17] are extended.