Let L be a general linear complex in PG(3, q) for any prime power q. We show that when GF(q) is extended to GF(q(2)), the extended lines of L cover a non-singular Hermitian surface H congruent to H(3, q(2)) of PG(3, q(2)). We prove that if S is any symplectic spread PG(3, q), then the extended lines of this spread form a complete (q(2) + 1)-span of H. Several other examples of complete spans of H for small values of q are also discussed. Finally, we discuss extensions to higher dimensions, showing in particular that a similar construction produces complete (q(3) + 1)-spans of the Hermitian variety H(5, q(2)).
Complete spans on Hermitian varieties / Aguglia, A.; Cossidente, A.; Ebert, G. L.. - In: DESIGNS, CODES AND CRYPTOGRAPHY. - ISSN 0925-1022. - 29:1-3(2003), pp. 7-15. [10.1023/A:1024179703511]
Complete spans on Hermitian varieties
Aguglia, A.;
2003-01-01
Abstract
Let L be a general linear complex in PG(3, q) for any prime power q. We show that when GF(q) is extended to GF(q(2)), the extended lines of L cover a non-singular Hermitian surface H congruent to H(3, q(2)) of PG(3, q(2)). We prove that if S is any symplectic spread PG(3, q), then the extended lines of this spread form a complete (q(2) + 1)-span of H. Several other examples of complete spans of H for small values of q are also discussed. Finally, we discuss extensions to higher dimensions, showing in particular that a similar construction produces complete (q(3) + 1)-spans of the Hermitian variety H(5, q(2)).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
