Title :
Optimal linear codes from matrix groups
Author :
Braun, Michael ; Kohnert, Axel ; Wassermann, Alfred
Author_Institution :
Dept. for IT Security, Siemens AG, Munich, Germany
Abstract :
New linear codes (sometimes optimal) over the finite field with q elements are constructed. In order to do this, an equivalence between the existence of a linear code with a prescribed minimum distance and the existence of a solution of a certain system of Diophantine linear equations is used. To reduce the size of the system of equations, the search for solutions is restricted to solutions with special symmetry given by matrix groups. This allows to find more than 400 new codes for the case q=2,3,4,5,7,9.
Keywords :
linear codes; matrix algebra; Diophantine linear equation; group of automorphism; incidence matrix; lattice point enumeration; linear code; minimum distance; system equation; Code standards; Equations; Error correction codes; Galois fields; Lattices; Linear code; Security; Upper bound; Vectors; Group of automorphisms; incidence matrix; lattice point enumeration; optimal linear code;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2005.859291
