MWS and FWS codes for coordinate-wise weight functions

A combinatorial problem concerning the maximum size of (Hamming) weight set an $$[n,k]_q$$ linear code was recently introduced. Codes attaining established upper bound are Maximum Weight Spectrum (MWS) codes. Those codes with same as $$\mathbb {F}_q^n$$ called Full (FWS) FWS necessarily “short”, whereas MWS “long”. For fixed k, q values n for which -FWS exists completely determined, but determination minimum length M(H, q) -MWS remains open problem. The current work broadens discussion first to general coordinate-wise functions, and then specifically Lee a Manhattan like weight. In case we provide bounds on exists, exists. When specializing or setting able determine parameters As Hamming case, $$M({\mathscr {L}},k,q)$$ (the codes), pose On other hand, respect