Fast decoding of quasi-perfect Lee distance codes

Authors:
Peter Horak;Bader F. Albdaiwi
Affiliations:
Interdisciplinary Arts and Sciences, University of Washington, Tacoma, USA;Department of Mathematics and Computer Science, Kuwait University, Kuwait
Venue:
Designs, Codes and Cryptography
Year:
2006

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Abstract

A code D over Z 2 n is called a quasi-perfect Lee distance-(2t + 1) code if d L(V,W) 驴 2t + 1 for every two code words V,W in D, and every word in Z 2 n is at distance 驴 t + 1 from at least one code word, where D L(V,W) is the Lee distance of V and W. In this paper we present a fast decoding algorithm for quasi-perfect Lee codes. The basic idea of the algorithm comes from a geometric representation of D in the 2-dimensional plane. It turns out that to decode a word it suffices to calculate its distance to at most four code words.