Claudio M. Qureshi

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cs.IT2018

On the non-existence of linear perfect Lee codes: The Zhang-Ge condition and a new polynomial criterion

Claudio Qureshi

The Golomb-Welch conjecture (1968) states that there are no $e$ -perfect Lee codes in $Z^{n}$ for $n \geq 3$ and $e \geq 2$ . This conjecture remains open even for linear codes.…

cs.IT2018

The set of dimensions for which there are no linear perfect 2-error-correcting Lee codes has positive density

Claudio Qureshi

The Golomb-Welch conjecture states that there are no perfect $e$ -error-correcting Lee codes in $Z^{n}$ ( $P L (n, e)$ -codes) whenever $n \geq 3$ and $e \geq 2$ . A special case of…