On Research Of The Intersection Sets In Finite Projective Space

This paper studies the (k,r)-arc of finite projective space, describes some important concepts in projective space PG(n,q)and coding theory.It introduces the related concept of finite projective spaces and coding theory and introduces the contact between them and some applications in coding theory.The maximum value of k for which a (k,r)-arc in PG(2,q) exists will be denoted by mr(2,q).The other two exact values of mr(2,q) is proved, that is:(I).mr(2,q)(r一1)q+1with q is a square and r=+1≥6；(II).mr(2,q)=(r一1)q+q-r with q=3h≥27,r=3h-3h-1).The upper bound of m2(4,q)(q is even and q>2)at some point will been amended,the previous results:when q is even and q>2,m2(4,q) where if q≥8,c=0；if q=4,c=-3.The corrected result:if q is even,and q=2e, P≥7,m2(4,q)≤q3-q2+15q-20.Also it gives the upper bound of m2(4,q)a greater improvement,i.e.m2(4,q)≤+q+2,(q≥16),and thereby resulting in improved m2(n,q)(q>2) upper bound,i.e.Whenn the result is better than the previous sector:m2(n,q)≤qn-1-(n-4)qn-2(n-3)21n-3,q≥18,4≤n≤2q/3.