The densest subgraph problem (DSG) aiming at finding an induced such that the average edge-weights of is maximized, a well-studied problem. However, when input graph hypergraph, existing notion DSG fails to capture fact hyperedge partially belonging sub-hypergraph also part sub-hypergraph. To resolve issue, we suggest function $$f_e:\mathbb {Z}_{\ge 0}\rightarrow \mathbb {R}_{\ge 0}$$ represent...

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 determi...