Every elliptic quartic C4 of PG(3, q) with n GF(q)-rational points provides a near-MDS code C of length n and dimension 4 such that the collineation group of C4 is isomorphic to the automorphism group of C. In this paper we assume that GF(q) has characteristic p>3. We classify the linear collineation groups of PG(3, q) which can preserve an elliptic quartic of PG(3, q). Also, we prove for q>112 that if the j-invariant of C4 does not disappear, then C cannot be extended in a natural way by addinga point of PG(3, q) to C4.
Near MDS codes araising from algebraic curves / Abatangelo, V.; Larato, B.. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - 301:1(2005), pp. 5-19. [10.1016/j.disc.2004.05.021]
Near MDS codes araising from algebraic curves
Abatangelo, V.;Larato, B.
2005-01-01
Abstract
Every elliptic quartic C4 of PG(3, q) with n GF(q)-rational points provides a near-MDS code C of length n and dimension 4 such that the collineation group of C4 is isomorphic to the automorphism group of C. In this paper we assume that GF(q) has characteristic p>3. We classify the linear collineation groups of PG(3, q) which can preserve an elliptic quartic of PG(3, q). Also, we prove for q>112 that if the j-invariant of C4 does not disappear, then C cannot be extended in a natural way by addinga point of PG(3, q) to C4.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
