TY - GEN
T1 - Weighted coverings and packings
AU - Cohen, Gérard
AU - Honkala, Iiro
AU - Litsyn, Simon
AU - Mattson, H. F.
PY - 1994
Y1 - 1994
N2 - We introduce a generalization of the concepts of coverings and packings in Hamming space called weighted coverings and packings. We study the existence of perfect weighted codes, discuss connections between weighted coverings and packings, and present many constructions for them. Conventional packings and coverings are arrangements of Hamming spheres of a given radius in the Hamming space. We generalize these concepts by attaching weights to different layers of the Hamming sphere. If several such spheres intersect in a point of the space we define the density at that point as the sum of the weights of the corresponding layers. We study the general problem of weighted packings (coverings) for which the density at each point is at most one (resp. at least one). We can consider several known types of codes, e.g., the uniformly packed codes, list codes, multiple coverings, L-codes, in a uniform way.
AB - We introduce a generalization of the concepts of coverings and packings in Hamming space called weighted coverings and packings. We study the existence of perfect weighted codes, discuss connections between weighted coverings and packings, and present many constructions for them. Conventional packings and coverings are arrangements of Hamming spheres of a given radius in the Hamming space. We generalize these concepts by attaching weights to different layers of the Hamming sphere. If several such spheres intersect in a point of the space we define the density at that point as the sum of the weights of the corresponding layers. We study the general problem of weighted packings (coverings) for which the density at each point is at most one (resp. at least one). We can consider several known types of codes, e.g., the uniformly packed codes, list codes, multiple coverings, L-codes, in a uniform way.
UR - http://www.scopus.com/inward/record.url?scp=84894369060&partnerID=8YFLogxK
U2 - 10.1109/ISIT.1994.394713
DO - 10.1109/ISIT.1994.394713
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AN - SCOPUS:84894369060
SN - 0780320158
SN - 9780780320154
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 305
BT - Proceedings - 1994 IEEE International Symposium on Information Theory, ISIT 1994
T2 - 1994 IEEE International Symposium on Information Theory, ISIT 1994
Y2 - 27 June 1994 through 1 July 1994
ER -