Codes of Desarguesian projective planes of even order, projective triads and [formula omitted]-arcs of type [formula omitted

Abstract

We study the binary dual codes associated with Desarguesian projective planes PG ( 2 , q ) , with q = 2 h , and their links with ( q + t , t ) -arcs of type ( 0 , 2 , t ) , by considering the elements of F q as binary h-tuples. Using a correspondence between ( q + t , t ) -arcs of type ( 0 , 2 , t ) and projective triads in PG ( 2 , q ) , q even, we present an alternative proof of the classification result on projective triads. We construct a new infinite family of ( q + t , t ) -arcs of type ( 0 , 2 , t ) with t = q 4 , using a particular form of the primitive polynomial of the field F q .