Codes of Desarguesian projective planes of even order, projective triads and (q+t,t)-arcs of type (0,2,t)

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 .

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