Perfect codes in the lp metric
نویسندگان
چکیده
We investigate perfect codes in Zn in the `p metric. Upper bounds for the packing radius r of a linear perfect code in terms of the metric parameter p and the dimension n are derived. For p = 2 and n = 2, 3, we determine all radii for which there exist linear perfect codes. The non-existence results for codes in Zn presented here imply non-existence results for codes over finite alphabets Zq, when the alphabet size is large enough, and have implications on some recent constructions of spherical codes.
منابع مشابه
Codes and lattices in the lp metric
Codes and associated lattices are studied in the lp metric, particularly in the l1 (Lee) and the l∞ (maximum) distances. Discussions and results on decoding processes, classification and analysis of perfect or dense codes in these metrics are presented. Keywords—Codes and lattices, lp metric, Lee metric, perfect codes.
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ورودعنوان ژورنال:
- Eur. J. Comb.
دوره 53 شماره
صفحات -
تاریخ انتشار 2016