New Codes Arising from Complete (k, n)- arcs in PG(3,17)

Abstract

The main aim of this work is to find new codes arising from construct a complete (k , n) – arcs in PG( 3,17), when n = 3,4,5 we take the union of some (k,n) – arcs. Furhtermore, when n = 6,7,8,…,307 by using matlab19B program (1) to found all construct a complete ( k , n + 1) - arcs from complete (k , n) - arcs. We start with points index zero and unit point, which we call the basic points of table (points and planes), then we start adding points from the remaining points of install the points of the first arc until we get intersections through which deleted all points of the plane , then we repeat that method until we get the maximum complete (5220 ; 307) - arcs. Then we find the [k, n, d] q-code of each a complete (k , n) - arcs  .

Keywords

• the main aim of this work is to find new codes arising from construct a complete (k , n) – arcs in pg( 3,17), when n = 3,4,5 we take the union of some (k,n) – arcs. furhtermore, when n = 6,7,8,…,307 by using matlab19b program (1) to found all c
• 307) - arcs. then we find the [k, n, d] q-code of each a complete (k , n) - arcs