Constructions of Cyclic and Quasi-Cyclic Grassmannian Codes

Linear random network coding is a newly created powerful scheme for information transmission in a network, which allows almost optimal performance. It has opened a significant research area not only in information technology, but also in discrete mathematics with widespread applications for communication networks like the Internet, wireless communication systems, and cloud computing. The construction of good network codes in some projective space is of highly mathematical nature and requires strong computational power for the resulting searches. In this paper was construct, using GAP System for Computational Discrete Algebra and Wolfram Mathematica, some cyclic Grassmannian codes, specially an optimal code over the finite field F-210. Also, it has been introduced the q-analogous of the classic quasi-cyclic block codes over finite fields, namely, the m-quasi-cyclic Grassmannian codes. Further, it was classified all the full length and degenerated orbits and quasi-orbits in the projective space P-q(n), for n up to 11.