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 ≅ H(3, q 2) of PG(3, q 2). We prove that if Sis 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).
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Aguglia, A., Cossidente, A. & Ebert, G.L. Complete Spans on Hermitian Varieties. Designs, Codes and Cryptography 29, 7–15 (2003). https://doi.org/10.1023/A:1024179703511
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DOI: https://doi.org/10.1023/A:1024179703511