On the completeness of certain n-tracks arising from elliptic curves
| Autor: | Fabio Pasticci, Massimo Giulietti |
|---|---|
| Jazyk: | angličtina |
| Předmět: |
Discrete mathematics
Algebra and Number Theory Applied Mathematics n-Tracks Sato–Tate conjecture General Engineering Near MDS codes Twists of curves Elliptic divisibility sequence Supersingular elliptic curve Theoretical Computer Science Projective spaces Half-period ratio Modular elliptic curve Jacobian curve Elliptic curves Schoof's algorithm Engineering(all) Mathematics |
| Zdroj: | Finite Fields and Their Applications. (4):988-1000 |
| ISSN: | 1071-5797 |
| DOI: | 10.1016/j.ffa.2006.09.007 |
| Popis: | Complete n-tracks in PG(N,q) and non-extendable Near MDS codes of dimension N+1 over Fq are known to be equivalent objects. The best known lower bound for the maximum number of points of an n-track is attained by elliptic n-tracks, that is, n-tracks consisting of the Fq-rational points of an elliptic curve. This has given a motivation for the study of complete elliptic n-tracks. From previous work, an elliptic n-track in PG(2,q) is complete provided that either the j-invariant j(E) of the underlying elliptic curve E is different from zero, or j(E)=0 and the number Nq of Fq-rational points of E is even. In this paper it is shown that the latter result extends to odd Nq if and only if either q is a square or p≡1(mod3), p being the characteristic of Fq. Some completeness results for elliptic n-tracks in dimensions 3 and 5 are also obtained. |
| Databáze: | OpenAIRE |
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