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Sets of type \((q+2,n)\) in PG(3, q)

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Abstract

We prove that if K is a set of type \((q+2,n)\) with \(n>q+2\) in PG(3, q), then \(n=2q+2\).

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References

  1. Calderbank, A.R., Kantor, J.M.: The geometry of two-weight codes. Bull. Lond. Math. Soc. 18, 97–122 (1986)

  2. Delsarte, P.: Weights of linear codes and strongly regular normed spaces. Discrete Math. 3, 47–64 (1972)

  3. Durante, N., Napolitano, V., Olanda, D.: Sets of type\((q, n)\) in \(PG(3, q)\). Ric. Mat. 65, 65–70 (2016). https://doi.org/10.1007/s11587-015-0252-x

  4. Durante, N., Napolitano, V., Olanda, D.: Sets of type\((q+1, n)\) in \(PG(3, q)\). J. Geom. 107, 9–18 (2016). https://doi.org/10.1007/s00022-015-0271-5

  5. Hirschfeld, J.W.P.: Finite Projective Spaces of Three Dimensions. Clarendon Press, Oxford (1985)

    MATH  Google Scholar 

  6. Innamorati, S., Zuanni, F.: On the parameters of two-intersection sets in\(PG(3, q)\). Atti Accad. Peloritana Pericol. 96(S2), 7 (2018)

  7. Tallini Scafati, M.: Sui\(k\)-insiemi di uno spazio di Galois\(S_{r, q}\)a due soli caratteri nella dimensione\(d\). Atti Accad. Peloritana Pericol. 60(6), 782–788 (1976)

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Correspondence to Fulvio Zuanni.

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Innamorati, S., Zannetti, M. & Zuanni, F. Sets of type \((q+2,n)\) in PG(3, q). J. Geom. 114, 22 (2023). https://doi.org/10.1007/s00022-023-00684-4

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  • DOI: https://doi.org/10.1007/s00022-023-00684-4

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