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 {C_{n}} be a sequence of binary linear codes of distance d_{n} and A_{dn} be the number of vectors of weight d_{n} in C_{n}, then log_{2} A_{dn} = 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. |