Institut de Mathématiques de Luminy

Abstract 2001-16

Alexei Ashikhmin, Alexander Barg, Serge Vladut.
Linear codes with exponentially many light vectors .

G. Kalai and N. Linial (1995) put forward the following conjecture: Let {Cn} be a sequence of binary linear codes of distance dn and Adn be the number of vectors of weight dn in Cn, then log2 Adn = o(n). We disprove this by constructing a family of linear codes from geometric Goppa codes in which the number of vectors of minimum weight grows exponentially with the length.



Last update : september 13, 2001, EL.