How many weights can a linear code have?

We study the combinatorial function L ( k , q ), the maximum number of nonzero weights a linear code of dimension k over F q can have. We determine it completely for q = 2 , and for k = 2 , and provide upper and lower bounds in the general case when both k and q are ≥ 3 . A refinement L ( n , k , q ), as well as nonlinear analogues N ( M , q ) and N ( n , M , q ), are also introduced and studied.