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Product Constructions for Perfect Lee Codes

Year: 2011

Type: article

Abstract: A well-known conjecture of Golomb and Welch is that the only nontrivial perfect codes in the Lee and Manhattan metrics have length two or minimum distance three. This problem and related topics were subject for extensive research in the last 40 years. In this paper, two product constructions for perfect Lee codes and diameter perfect Lee codes are presented. These constructions yield a large number of nonlinear perfect codes and nonlinear diameter perfect codes in the Lee and Manhattan metrics. A short survey and other related problems on perfect codes in the Lee and Manhattan metrics are also discussed.

Source: IEEE Transactions on Information Theory

DOI: 10.1109/tit.2011.2161133

Author: Tuvi Etzion

Institution: Technion – Israel Institute of Technology

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2154119782

FWCI: 2.941

Cites: 34

Cited by: 31

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