Linear codes with exponentially many light vectors
01 November 2001
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 $A_{d_n}$ be the number of vectors of weight $d_n$ in $C_n$, then $log_2 A_{d_n}=o(n).$ 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.
