Abstract
A set of n + k points (k > 0) in projective space of dimension n is said to be an (n + k)-arc if there is no hyperplane containing any n + 1 points of the set. It is well-known that for the projective space PG(n, q), this is equivalent to a maximum distance separable linear code with symbols in the finite field GF(q), of length n + k, dimension n + 1, and distance d = k that satisfies the Singleton bound d ≤ k. We give an algebraic condition for such a code, or set of points, and this is associated with an identity involving determinants.
Original language | English |
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Pages (from-to) | 215-218 |
Number of pages | 4 |
Journal | Designs Codes and Cryptography |
Volume | 58 |
Issue number | 2 |
DOIs | |
Publication status | Published - Feb 2011 |
Keywords
- Arc
- Determinant
- General position
- Grassmannian
- MDS code
- Projective space