New quasi-cyclic codes from finite upper half-planes. (13th October 2020)

• Record Type: Journal Article
• Authors: Silva, Eduardo Brandani Da; Castelani, Emerson Vitor; Carneiro, Maycow Gonçalves
• Is Part Of: International journal of information and coding theory. Volume 5:Number 3/4(2020)
• Page Start: 239
• Page End: 265
• Publication Date: 2020-10-13
• Subjects: error-correcting codes -- quasi-cyclic codes -- upper half-planes -- finite fields -- decoding; Coding theory -- Periodicals; Information theory -- Periodicals; 003.54
• Languages: English
• ISSNs: 1753-7703

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.