On some perfect codes with respect to Lee metric

✍ Scribed by Sapna Jain; Ki-Bong Nam; Ki-Suk Lee

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 226 KB
• Volume: 405
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2005.03.001

✦ Synopsis

In this paper, we obtain bounds on the number of parity check digits for Lee weight codes correcting errors of Lee weight 1, errors of Lee weight 2 or less, errors of Lee weight 3 or less and errors of Lee weight 4 or less over Z q (q 5, a prime) respectively. We also examine these bounds with equality to check for perfect codes and have shown the existence of perfect codes correcting errors of Lee weight 1 over Z 5 and perfect codes correcting errors of Lee weight 2 or less over Z 13 . We have also shown the nonexistence of perfect codes correcting errors of Lee weight 2 or less over Z q when q = 4n + 3 (q prime) and correcting errors of Lee weight 3 or less and errors of Lee weight 4 or less over Z q (5 q 97, a prime). We further conjecture that there does not exist a perfect code correcting errors of Lee weight t or less (t 3) over Z q (q 5, a prime).