کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9498388 | 1631196 | 2005 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On some perfect codes with respect to Lee metric
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
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 Zq (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 Z5 and perfect codes correcting errors of Lee weight 2 or less over Z13. We have also shown the nonexistence of perfect codes correcting errors of Lee weight 2 or less over Zq when q = 4n + 3 (q prime) and correcting errors of Lee weight 3 or less and errors of Lee weight 4 or less over Zq (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 Zq (q ⩾ 5, a prime).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 405, 1 August 2005, Pages 104-120
Journal: Linear Algebra and its Applications - Volume 405, 1 August 2005, Pages 104-120
نویسندگان
Sapna Jain, Ki-Bong Nam, Ki-Suk Lee,