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Designs, Codes and Cryptography

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19-03-2019

Generalized binary arrays from quasi-orthogonal cocycles

Authors: J. A. Armario, D. L. Flannery

Published in: Designs, Codes and Cryptography | Issue 10/2019

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Abstract

Generalized perfect binary arrays (GPBAs) were used by Jedwab to construct perfect binary arrays. A non-trivial GPBA can exist only if its energy is 2 or a multiple of 4. This paper introduces generalized optimal binary arrays (GOBAs) with even energy not divisible by 4, as analogs of GPBAs. We give a procedure to construct GOBAs based on a characterization of the arrays in terms of 2-cocycles. As a further application, we determine negaperiodic Golay pairs arising from generalized optimal binary sequences of small length.

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Álvarez V., Armario J.A., Frau M.D., Real P.: A system of equations for describing cocyclic Hadamard matrices. J. Comb. Des. 16, 276–290 (2008).MathSciNetCrossRefMATH

Arasu K.J., Chen Y.Q., Pott A.: Hadamard and conference matrices. J. Algebr. Comb. 14, 103–117 (2001).MathSciNetCrossRefMATH

Armario J.A., Flannery D.L.: On quasi-orthogonal cocycles. J. Comb. Des. 26, 401–411 (2018).MathSciNetCrossRef

Balonin N., Djokovic D.: Negaperiodic Golay pairs and Hadamard matrices. Inf. Control Syst. 5, 2–17 (2015).

Carlet C., Ding C.: Highly nonlinear mappings. J. Complexity 20, 205–244 (2004).MathSciNetCrossRefMATH

de Launey W., Flannery D.L., Horadam K.J.: Cocyclic Hadamard matrices and difference sets. Discret. Appl. Math. 102, 47–62 (2000).MathSciNetCrossRefMATH

de Launey W., Flannery D.L.: Algebraic Design Theory. Mathematical Surveys and Monographs, vol. 175. American Mathematical Society, Providence, RI (2011).

Egan R.: On equivalence of negaperiodic Golay pairs. Des. Codes Cryptogr. 85, 523–532 (2017).MathSciNetCrossRefMATH

Flannery D.L.: Cocyclic Hadamard matrices and Hadamard groups are equivalent. J. Algebra 192, 749–779 (1997).MathSciNetCrossRefMATH

10.

Hiramine Y.: On \((2n,2,2n, n)\)-relative difference sets. J. Comb. Theory Ser. A 101, 281–284 (2003).MathSciNetCrossRefMATH

11.

Hughes G.: Non-splitting abelian \((4t,2,4t, 2t)\) relative difference sets and Hadamard cocycles. Eur. J. Combin. 21, 323–331 (2000).MathSciNetCrossRefMATH

12.

Ito N.: On Hadamard groups. J. Algebra 168, 981–987 (1994).MathSciNetCrossRefMATH

13.

Ito N.: On Hadamard groups III. Kyushu J. Math. 51, 369–379 (1997).MathSciNetCrossRefMATH

14.

Jedwab J.: Generalized perfect arrays and Menon difference sets. Des. Codes Cryptogr. 2, 19–68 (1992).MathSciNetCrossRefMATH

15.

Pott A.: Nonlinear functions in abelian groups and relative difference sets. Discret. Appl. Math. 138, 177–193 (2004).MathSciNetCrossRefMATH

16.

Schmidt B.: Williamson matrices and a conjecture of Ito’s. Des. Codes Cryptogr. 17, 61–68 (1999).MathSciNetCrossRefMATH

Title: Generalized binary arrays from quasi-orthogonal cocycles
Authors: J. A. Armario
D. L. Flannery
Publication date: 19-03-2019
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 10/2019
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-019-00626-9

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Generalized binary arrays from quasi-orthogonal cocycles

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