A group theoretic characterization of classical unitals
Giorgio Donati
and Nicola Durante
Università di Napoli “Federico II”, Via Cintia, 80126 Naples, Italy
DOI: 10.1007/s10801-011-0322-4
Abstract
Let G be the group of projectivities stabilizing a unital U \mathcal{U} in PG(2, q 2). In this paper, we prove that U \mathcal{U} is a classical unital if and only if there are two points in U \mathcal{U} such that the stabilizer of these two points in G has order q 2 - 1.
Pages: 33–43
Keywords: keywords unitals; Hermitian curves; Reed-muller codes
Full Text: PDF
References
1. Abatangelo, L.M.: Una caratterizzazione gruppale delle curve hermitiane. Matematiche 39, 101-110 (1984)
2. Assmus, E.F. Jr., Key, J.D.: Designs and Their Codes. Cambridge University Press, Cambridge (1992)
3. Barwick, S.G., Ebert, G.L.: Unitals in Projective Planes. Springer Monographs in Mathematics. Springer, New York (2008)
4. Bruen, A.A., Forcinito, M.A.: Cryptography, Information Theory and Error-Correction. Wiley- Interscience, New York (2006)
5. Casse, L.R.A., O'Keefe, C.M., Penttila, T.: Characterizations of Buekenhout-Metz unitals. Geom. Dedic. 59, 29-42 (1996)
6. Cossidente, A., Ebert, G.L., Korchmáros, G.: A group theoretic characterization of classical unitals. Arch. Math. 74, 1-5 (2000)
7. Cossidente, A., Ebert, G.L., Korchmáros, G.: Unitals in finite Desarguesian planes. J. Algebr. Comb. 14, 119-125 (2001)
8. Ebert, G.L., Wantz, K.: A group theoretic characterization of Buekenhout-Metz unitals. J. Comb. Des.
2. Assmus, E.F. Jr., Key, J.D.: Designs and Their Codes. Cambridge University Press, Cambridge (1992)
3. Barwick, S.G., Ebert, G.L.: Unitals in Projective Planes. Springer Monographs in Mathematics. Springer, New York (2008)
4. Bruen, A.A., Forcinito, M.A.: Cryptography, Information Theory and Error-Correction. Wiley- Interscience, New York (2006)
5. Casse, L.R.A., O'Keefe, C.M., Penttila, T.: Characterizations of Buekenhout-Metz unitals. Geom. Dedic. 59, 29-42 (1996)
6. Cossidente, A., Ebert, G.L., Korchmáros, G.: A group theoretic characterization of classical unitals. Arch. Math. 74, 1-5 (2000)
7. Cossidente, A., Ebert, G.L., Korchmáros, G.: Unitals in finite Desarguesian planes. J. Algebr. Comb. 14, 119-125 (2001)
8. Ebert, G.L., Wantz, K.: A group theoretic characterization of Buekenhout-Metz unitals. J. Comb. Des.
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