Title of article :
Linear Codes with Exponentially Many Light Vectors
Author/Authors :
Ashikhmin، نويسنده , , Alexei and Barg، نويسنده , , Alexander and Vl?du?، نويسنده , , Serge، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2001
Abstract :
G. Kalai and N. Linial (1995, IEEE Trans. Inform. Theory41, 1467–1472) 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.
Journal title :
Journal of Combinatorial Theory Series A
Journal title :
Journal of Combinatorial Theory Series A
