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

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-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.