3 years ago

How many weights can a linear code have?

Minjia Shi, Hongwei Zhu, Patrick Solé, Gérard D. Cohen


We study the combinatorial function L(kq),  the maximum number of nonzero weights a linear code of dimension k over \({\mathbb {F}}_q\) 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 \(\ge 3.\) A refinement L(nkq),  as well as nonlinear analogues N(Mq) and N(nMq),  are also introduced and studied.

Open access
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