Title :
Linear codes with covering radius 2, 3 and saturating sets in projective geometry
Author :
Davydov, Alexander A. ; Marcugini, Stefano ; Pambianco, Fernanda
Author_Institution :
Inst. for Inf. Transmission Problems, Russian Acad. of Sci., Moscow, Russia
fDate :
3/1/2004 12:00:00 AM
Abstract :
Infinite families of linear codes with covering radius R=2, 3 and codimension tR+1 are constructed on the base of starting codes with codimension 3 and 4. Parity-check matrices of the starting codes are treated as saturating sets in projective geometry that are obtained by computer search using projective properties of objects. Upper bounds on the length function and on the smallest sizes of saturating sets are given.
Keywords :
geometry; linear codes; matrix algebra; parity check codes; computer search; covering radius; linear codes; parity-check matrices; projective geometry; saturating sets; Computational geometry; Error correction codes; Galois fields; Informatics; Linear code; Mathematics; Parity check codes; Upper bound; Vectors;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2004.825503
