Full weight spectrum one-orbit cyclic subspace codes

TL;DR

This paper classifies one-orbit cyclic subspace codes with full weight spectrum, extending the concept of maximum weight diversity from classical codes to subspace codes in network coding.

Contribution

It provides a complete classification of full weight spectrum one-orbit cyclic subspace codes using number theory and combinatorics.

Findings

Complete classification of full weight spectrum one-orbit cyclic subspace codes

Extension of maximum weight spectrum concept to subspace codes

Application relevance in network coding error correction

Abstract

For a linear Hamming metric code of length n over a finite field, the number of distinct weights of its codewords is at most n. The codes achieving the equality in the above bound were called full weight spectrum codes. In this paper we will focus on the analogous class of codes within the framework of cyclic subspace codes. Cyclic subspace codes have garnered significant attention, particularly for their applications in random network coding to correct errors and erasures. We investigate one-orbit cyclic subspace codes that are full weight spectrum in this context. Utilizing number theoretical results and combinatorial arguments, we provide a complete classification of full weight spectrum one-orbit cyclic subspace codes.