Classification of perfect codes and minimal distances in the Lee metric
نویسنده
چکیده
Perfect codes and minimal distance of a code have great importance in the study of theory of codes. The perfect codes are classified generally and in particular for the Lee metric. However, there are very few perfect codes in the Lee metric. The Lee metric has nice properties because of its definition over the ring of integers residue modulo q. It is conjectured that there are no perfect codes in this metric for q > 3, where q is a prime number. The minimal distance comes into play when it comes to detection and correction of error patterns in a code. A few bounds on the number of codewords and minimal distance of a code are discussed. Some examples for the codes are constructed and their minimal distance is calculated. The bounds are illustrated with the help of the results obtained. Key-words: Hamming metric; Lee metric; Perfect codes; Minimal distance
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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