A generalization of Lee codes
نویسندگان
چکیده
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 s will be shown. In addition, an extension of the long-standing Golomb-Welch conjecture, in terms of PDDS, will be stated. We note that all constructed PDDS s are lattice-like which is a very important feature from the practical point of view as in this case decoding algorithms tend to be much simpler. This paper is dedicated to the memory of Lucia Gionfriddo. Mathematics Subject Classification (2000) MSC Primary 05C69 · MSC Secondary 94B25
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عنوان ژورنال:
- Des. Codes Cryptography
دوره 70 شماره
صفحات -
تاریخ انتشار 2014