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Optimal linear codes from matrix groups

Title data

Braun, Michael ; Kohnert, Axel ; Wassermann, Alfred:
Optimal linear codes from matrix groups.
In: IEEE Transactions on Information Theory. Vol. 51 (December 2005) Issue 12 . - pp. 4247-4251.
ISSN 0018-9448
DOI: https://doi.org/10.1109/TIT.2005.859291

Abstract in another language

New linear codes (sometimes optimal) over the finite field with 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 = 2, 3, 4, 5, 7, 9.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Group of automorphisms; incidence matrix; lattice point enumeration; optimal linear code
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics and Didactics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 22 Jan 2015 15:10
Last Modified: 22 Jan 2015 15:10
URI: https://eref.uni-bayreuth.de/id/eprint/5799