Title :
On the size of arcs in projective spaces
Author :
Ali, A.H. ; Hirschfeld, J.W.P. ; Kaneta, H.
Author_Institution :
Sch. of Math. & Phys. Sci., Sussex Univ., Brighton, UK
fDate :
11/1/1995 12:00:00 AM
Abstract :
The known results on the maximum size of an arc in a projective space or equivalently the maximum length of a maximum distance separable linear code are surveyed. It is then shown that this maximum is q+1 for all dimensions up to q in the cases that q=11 and q=13; the result for q=11 was previously known. The strategy is to first show that a 11-arc in PG (3,11) and a 12-arc in PG (3,13) are subsets of a twisted cubic, that is, a normal rational curve
Keywords :
algebraic geometric codes; linear codes; MDS code; maximum arc size; maximum distance separable linear code; normal rational curve; projective space; twisted cubic; Galois fields; Helium; Linear code; Polynomials; Symmetric matrices; Tin; Vectors;
Journal_Title :
Information Theory, IEEE Transactions on
