How many weights can a linear code have?
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We study the combinatorial function L(k,q), the maximum number of nonzero weights a linear code of dimension k over _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.
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