ON THE CONSTRUCTION OF PERFECT CODES
FOR n-DIMENSIONAL INTERLEAVING
Cibele Cristina Trinca1, Reginaldo Palazzo Junior2
1Federal University of Tocantins (UFT)
Department of Biotechnology
and Bioprocess Engineering
Rua Badejós, Lote 7, Chácaras 69/72
Gurupi-TO - 77402-970, BRAZIL
2State University of Campinas (UNICAMP)
Department of Telematics
Av. Albert Einstein, 400
Cidade Universitária “Zeferino Vaz”
Campinas-SP - 13081-970, BRAZIL

Abstract

The authors propose an $n$-dimensional interleaving technique which spreads a cluster of errors having a quasicircular shape. Consequently simple one-dimensional random-error-correcting codes can be used to correct this kind of cluster instead of the more complex $n$-dimensional burst-error-correcting codes. Moreover let $p\geq 2$ be a positive integer, whenever $n\neq 1 \ mod \ 3$, the corresponding $n$-dimensional interleaving technique provides a perfect code. Also, whenever $n=3p-2=1 \ mod \ 3$, the corresponding $n$-dimensional interleaving technique provides neither a perfect code nor a quasi-perfect code.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 34
Issue: 3
Year: 2021

DOI: 10.12732/ijam.v34i3.5

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