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Results on error-correcting codes obtained using linear algebra

Author
Ball, S.
Type of activity
Presentation of work at congresses
Name of edition
Real Sociedad Matematica Española
Date of publication
2013
Presentation's date
2013-01-23
Book of congress proceedings
Sesiones Especiales - RSME 2013
First page
16
Last page
16
Abstract
A linear code C is a k-dimensional subspace of Fnq, with respect to a fixed basis. Let d 2 N be minimal sich that every non-zero vector of C has at least d non-zero coordinates. With such a code, up to b(d ¿ 1)=2c errors in any codeword can be corrected when sending codewords down a noisy channel. There are many results on error-correcting codes obtained by combinatorial arguments (and these generally apply to non-linear codes as well) such as the sphere packing bound, the Gilbert-Varshamov bou...
Group of research
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

Participants