Finding Cliques in Projective Space: A Method for Construction of Cyclic Grassmannian Codes

Finding Cliques in Projective Space: A Method for Construction of Cyclic Grassmannian Codes

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In general, the construction of subspace codes or, in particular, cyclic Grassmannian codes in some projective space Pq(n) is highly mathematical and requires substantial 1.29x4 computational power for the resulting searches.In this paper, we present a new method for the construction of cyclic Grassmannian codes.To do that was designed and implemented a series of algorithms using the GAP System for Computational Discrete Algebra and Wolfram m7 mega truck Mathematica software.We also present a classification of such codes in the space Pq(n), with n at most 9.

The fundamental idea to construct and classify the cyclic Grassmannian codes is to endow the projective space Pq(n) with a graph structure and then find cliques.