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Finding Cliques in Projective Space: A Method for Construction of Cyclic Grassmannian Codes
IEEE Access ( IF 4.098 ) Pub Date : 2020-03-13 , DOI: 10.1109/access.2020.2980670
Ismael Gutiérrez-García; Ivan Molina Naizir

In general, the construction of subspace codes or, in particular, cyclic Grassmannian codes in some projective space $\mathbb {P}_{q}(n)$ is highly mathematical and requires substantial 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 Mathematica software. We also present a classification of such codes in the space $\mathbb {P}_{q}(n)$ , with $n$ at most 9. The fundamental idea to construct and classify the cyclic Grassmannian codes is to endow the projective space $\mathbb {P}_{q}(n)$ with a graph structure and then find cliques.
更新日期:2020-03-24

 

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