Characterization of some optimal arcs (Q2275885)

The subject of this paper concerns the nonexistence of arcs with parameters \((398,101)\), \((464, 117)\) and \((467,118)\) in \(PG(4,4)\). The proof relies on the geometric characterization of \((117,30)-\) and \((118,30)\)-arcs in \(PG(3,4)\). This settles the problem of finding the exact value of \(n_4(5,d)\), the minimal length of a \(5\)-dimensional linear code of minimum distance \(d\) over the field with \(4\) elements, for eight values of \(d\): \(297, 298, 347, 348, 349, 350, 351, 352\).