Title: New quasi-cyclic codes from finite upper half-planes

Authors: Eduardo Brandani Da Silva; Emerson Vitor Castelani; Maycow Gonçalves Carneiro

Addresses: Departamento de Matemática, Universidade Estadual de Maringá – UEM, Av. Colombo 5790, Maringá – PR, 870300-110, Brazil ' Departamento de Matemática, Universidade Estadual de Maringá – UEM, Av. Colombo 5790, Maringá – PR, 870300-110, Brazil ' UTFPR – Câmpus Francisco Beltrão, Linha Santa Barbara s/n, Francisco Beltrão – PR, 85601-970, Brazil

Abstract: Finite upper half-planes can be seen as a natural environment to generate error-correcting codes. Current work analyses some properties of these spaces to generate new classes of quasi-cyclic error-correcting codes. These codes may be generated using the norm or the distance in these spaces. Using properties of the sets, we also propose a decoding algorithm.

Keywords: error-correcting codes; quasi-cyclic codes; upper half-planes; finite fields; decoding.

DOI: 10.1504/IJICOT.2020.110737

International Journal of Information and Coding Theory, 2020 Vol.5 No.3/4, pp.239 - 265

Received: 20 Dec 2019
Accepted: 27 May 2020

Published online: 13 Oct 2020 *

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