On the Characterization of (3 mod 5) Arcs

In this note we charcterize all (3 mod 5)-arcs in PG(2, 5) of cardinality 18, 23, 28, 33, and 38. This characterization is used further to prove that every (3 mod 5)-arc in PG(3, 5) of cardinality at most 158 is lifted. This result is instrumental in prosving the nonexistence of the hypothetical [104, 4, 82]5 and [204, 4, 162]5-codes.