2012/10/21 by Tuvi Etzion, Etzion, Tuvi, Alexander Vardy +3
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.IT
paper · pdf · doi:10.48550/arxiv.1210.5725
openalex publication_date 2012/10/21 · arxiv created 2012/12/11 · arxiv updated 2012/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper has two goals. The first one is to discuss good codes for packing problems in the Lee and Manhattan metrics. The second one is to consider weighing matrices for some of these coding problems. Weighing matrices were considered as building blocks for codes in the Hamming metric in various constructions. In this paper we will consider mainly two types of weighing matrices, namely conference matrices and Hadamard matrices, to construct codes in the Lee (and Manhattan) metric. We will show that these matrices have some desirable properties when considered as generator matrices for codes in these metrics. Two related packing problems will be considered. The first is to find good codes for error-correction (i.e. dense packings of Lee spheres). The second is to transform the space in a way that volumes are preserved and each Lee sphere (or conscribed cross-polytope), in the space, will be transformed to a shape inscribed in a small cube.