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

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4851))

Abstract

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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References

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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. Dillon, J.F., McGuire, G.: Kasami-Welch Functions on a Hyperplane (submitted)

    Google Scholar 

  4. Delsarte, P., Goethals, J.M.: Alternating Bilinear Forms over GF(q). J. Comb. Th. Ser. A 19, 26–50 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  5. Gow, R., Quinlan, R.: On the Vanishing of Subspaces of Alternating Bilinear Forms. Linear and Multilinear Algebra 54, 415–428 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  6. Gow, R., Quinlan, R.: Galois Extensions and Subspaces of Alternating Bilinear Forms with Special Rank Properties (submitted)

    Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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. Petrovic, Z.: Nonsingular Bilinear Maps, Spaces of Matrices, Immersions and Embeddings. In: Contemporary Geometry and Related Topics, Belgrade (2006), http://www.emis.de/proceedings/CGRT2005/

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Serdar BoztaÅŸ Hsiao-Feng (Francis) Lu

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© 2007 Springer-Verlag Berlin Heidelberg

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McGuire, G. (2007). Spectra of Boolean Functions, Subspaces of Matrices, and Going Up Versus Going Down. In: BoztaÅŸ, S., Lu, HF.(. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2007. Lecture Notes in Computer Science, vol 4851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77224-8_5

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  • DOI: https://doi.org/10.1007/978-3-540-77224-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77223-1

  • Online ISBN: 978-3-540-77224-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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