منابع مشابه
On diameter perfect constant-weight ternary codes
From cosets of binary Hamming codes we construct diameter perfect constantweight ternary codes with weight n − 1 (where n is the code length) and distances 3 and 5. The class of distance 5 codes has parameters unknown before.
متن کاملQuasi-Perfect Lee Codes from Quadratic Curves over Finite Fields
Golomb and Welch conjectured in 1970 that there only exist perfect Lee codes for radius t = 1 or dimension n = 1, 2. It is admitted that the existence and the construction of quasi-perfect Lee codes have to be studied since they are the best alternative to the perfect codes. In this paper we firstly highlight the relationships between subset sums, Cayley graphs, and Lee linear codes and present...
متن کاملOn the nonexistence of linear perfect Lee codes
In 1968, Golomb and Welch conjectured that there does not exist perfect Lee code in Z with radius r ≥ 2 and dimension n ≥ 3. Besides its own interest in coding theory and discrete geometry, this conjecture is also strongly related to the degree-diameter problems of abelian Cayley graphs. Although there are many papers on this topic, the Golomb-Welch conjecture is far from being solved. In this ...
متن کاملClassification of perfect codes and minimal distances in the Lee metric
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 ...
متن کاملWeighted codes in Lee metrics
Perfect weighted coverings of radius one have been often studied in the Hamming metric. In this paper, we study these codes in the Lee metric. To simplify the notation, we use a slightly different description, yet equivalent. Given two integers a and b , an (a, b)-code is a set of vertices such that vertices in the code have a neighbours in the code and other vertices have b neighbours in the c...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2012
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2012.2196257