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

In general, the construction of subspace codes or, in particular, cyclic Grassmannian codes in some projective space 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 Grassmann...

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Bibliographic Details
Published inIEEE access Vol. 8; pp. 51333 - 51339
Main Authors Gutierrez-Garcia, Ismael, Naizir, Ivan Molina
Format Journal Article
LanguageEnglish
Published Piscataway IEEE 2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Algorithms
Classification algorithms
Cliques
cyclic codes
finite fields
Grassmannian codes
Information theory
Mathematical analysis
Object recognition
Orbits
projective space
Space vehicles
subspace codes
Tungsten
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Summary:In general, the construction of subspace codes or, in particular, cyclic Grassmannian codes in some projective space 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 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 P q (n) with a graph structure and then find cliques.
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2020.2980670