A generalization of Lee codes
نویسندگان
چکیده
منابع مشابه
A generalization of Lee codes
Motivated by a problem in computer architecture we introduce a notion of the perfect distance-dominating set, PDDS, in a graph. PDDS s constitute a generalization of perfect Lee codes, diameter perfect codes, as well as other codes and dominating sets. In this paper we initiate a systematic study of PDDS s. PDDS s related to the application will be constructed and the non-existence of some PDDS...
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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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Carlet [2] has determined the linear codes over Z=(4) of constant Lee weight. This extended abstract describes a di erent approach to this problem, along the lines of [4], which has the potential to apply to a wide class of examples. In particular, we show that linear codes of constant Lee or Euclidean weight seldom exist over Z=(p) when p is an odd prime. Over nite elds, any linear code with c...
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2012
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-012-9666-6