TY - GEN
T1 - Coding for the Lee and Manhattan metrics with weighing matrices
AU - Etzion, Tuvi
AU - Vardy, Alexander
AU - Yaakobi, Eitan
PY - 2013
Y1 - 2013
N2 - 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 one is to find good codes for error-correction (i.e. dense packings of Lee spheres). The second one 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 into a shape inscribed in a small cube.
AB - 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 one is to find good codes for error-correction (i.e. dense packings of Lee spheres). The second one 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 into a shape inscribed in a small cube.
UR - https://www.scopus.com/pages/publications/84890330878
U2 - 10.1109/ISIT.2013.6620275
DO - 10.1109/ISIT.2013.6620275
M3 - Conference contribution
SN - 9781479904464
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 494
EP - 498
BT - 2013 IEEE International Symposium on Information Theory, ISIT 2013
T2 - 2013 IEEE International Symposium on Information Theory, ISIT 2013
Y2 - 7 July 2013 through 12 July 2013
ER -