Spectra of Boolean Functions, Subspaces of Matrices, and Going Up Versus Going Down

  • Gary McGuire
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4851)


We will discuss two different but related topics. We first give a connection between the Fourier spectrum of Boolean functions and subspaces of skew-symmetric subspaces where each nonzero element has a lower bound on its rank. Secondly, we discuss some connections between bent and near-bent functions.


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  1. 1.
    Canteaut, A., Carlet, C., Charpin, P., Fontaine, C.: On Cryptographic Properties of the Cosets of R(1,m). IEEE Trans. Inform. Theory 47(4), 1494–1513 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Calderbank, A.R., Diggavi, S.N., Al-Dhahir, N.: Space-Time Signaling Based on Kerdock and Delsarte-Goethals Codes. In: IEEE ICC 2004, vol. 1, pp. 483–487 (2004)Google Scholar
  3. 3.
    Dillon, J.F., McGuire, G.: Kasami-Welch Functions on a Hyperplane (submitted)Google Scholar
  4. 4.
    Delsarte, P., Goethals, J.M.: Alternating Bilinear Forms over GF(q). J. Comb. Th. Ser. A 19, 26–50 (1975)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Gow, R., Quinlan, R.: On the Vanishing of Subspaces of Alternating Bilinear Forms. Linear and Multilinear Algebra 54, 415–428 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Gow, R., Quinlan, R.: Galois Extensions and Subspaces of Alternating Bilinear Forms with Special Rank Properties (submitted)Google Scholar
  7. 7.
    Lu, H.F.F., Kumar, P.V.: Rate-Diversity Tradeoff of Space-Time Codes with Fixed Alphabet and Optimal Constructions for PSK Modulation. IEEE Trans. Inform. Theory 49(10), 2747–2751 (2003)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Lahtonen, J., McGuire, G., Ward, H.N.: Gold and Kasami-Welch Functions, Quadratic Forms, and Bent Functions. In: Advances in Mathematics of Communications (2007)Google Scholar
  9. 9.
    Petrovic, Z.: Nonsingular Bilinear Maps, Spaces of Matrices, Immersions and Embeddings. In: Contemporary Geometry and Related Topics, Belgrade (2006),

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Gary McGuire
    • 1
  1. 1.School of Mathematical Sciences, University College DublinIreland

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