Existence Of (47,5)- Arcs in The Projective Plane PG (2,13)

In this work we show the existence of complete (47,5)- arcs which are unknown until now. The upper bound for the (k,5)- arcs is narrowed in the finite projective plane PG (2,13). The narrowing is fulfilled by finding complete (47,5)-arcs which are 372 arcs. However, only one (47,5)-complete arc out of the 372 is considered in this work. Furthermore the relation between complete (k, n)-arcs and minimal t-blocking sets is proved, in addition to between the connection of our arc and the code.