On the construction of perfect codes from HEX signal constellations

Trinca, Cibele Cristina; Carvalho, Edmir Daniel; Filho, Jozué Vieira; Andrade, Antonio Aparecido de

doi:10.1016/j.jfranklin.2012.09.007

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Three-dimensional Interleaving1

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2021

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“…Therefore, in this case, we have a perfect code [12]. Other approaches on the construction of perfect codes can be found in [15,16].…”

Section: Three-dimensional Interleavingmentioning

confidence: 99%

ON THE CONSTRUCTION OF PERFECT CODES FOR $n$-DIMENSIONAL INTERLEAVING

Trinca¹,

Junior²

2021

Int. J. of Appl. Math.

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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-errorcorrecting codes. Moreover let p ≥ 2 be a positive integer, whenever n = 1 mod 3, the corresponding n-dimensional interleaving technique provides a perfect code. Also, whenever n = 3p − 2 = 1 mod 3, the corresponding ndimensional interleaving technique provides neither a perfect code nor a quasiperfect code.

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“…Therefore, in this case, we have a perfect code [12]. Other approaches on the construction of perfect codes can be found in [15,16].…”

Section: Three-dimensional Interleavingmentioning

confidence: 99%