nach oben

Designs, Codes and Cryptography

Erschienen in:

16.09.2017

Unbiased orthogonal designs

verfasst von: Hadi Kharaghani, Sho Suda

Erschienen in: Designs, Codes and Cryptography | Ausgabe 7/2018

Einloggen, um Zugang zu erhalten

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

The notion of unbiased orthogonal designs is introduced as a generalization of unbiased Hadamard matrices, unbiased weighing matrices and quasi-unbiased weighing matrices. We provide upper bounds and several methods of construction for mutually unbiased orthogonal designs. As an application, mutually quasi-unbiased weighing matrices for various parameters are obtained.

Vorheriger Artikel On MDS linear complementary dual codes and entanglement-assisted quantum codes

Agaian S.S.: Hadamard Matrices and Their Applications, vol. 1168. Lecture Notes in Mathematics. Springer, Berlin (1985).

Araya M., Harada M., Suda S.: Quasi-unbiased Hadamard matrices and weakly unbiased Hadamard matrices: a coding-theoretic approach. Math. Comput. 304, 951–984 (2017).MathSciNetMATH

Best D., Kharaghani H., Ramp H.: Mutually unbiased weighing matrices. Des. Codes Cryptogr. 76, 237–256 (2015).MathSciNetCrossRefMATH

Bose R.C.: Strongly regular graphs, partial geometries and partially balanced designs. Pac. J. Math. 13, 389–419 (1963).MathSciNetCrossRefMATH

Bush K.A.: Unbalanced Hadamard matrices and finite projective planes of even order. J. Comb. Theory Ser. A 11, 38–44 (1971).MathSciNetCrossRefMATH

Butson A.T.: Generalized Hadamard matrices. Proc. Am. Math. Soc. 13, 894–898 (1962).MathSciNetCrossRefMATH

Geramita A.V., Seberry J.: Orthogonal Designs. Quadratic Forms and Hadamard Matrices, vol. 45. Lecture Notes in Pure and Applied Mathematics. Marcel Dekker, Inc., New York (1979).

Haemers W.H., Tonchev V.D.: Spreads in strongly regular graphs. Des. Codes Cryptogr. 8, 145–157 (1996).MathSciNetMATH

Holzmann W.H., Kharaghani H., Orrick W.: On the Real Unbiased Hadamard Matrices. Combinatorics and Graphs. Contemporary Mathematics, vol. 531. American Mathematical Society, Providence, RI (2010).MATH

10.

Kharaghani H.: New class of weighing matrices. Ars Comb. 19, 69–72 (1985).MathSciNetMATH

11.

Kharaghani H., Sasani S., Suda S.: Mutually unbiased Bush-type Hadamard matrices and association schemes. Electron. J. Comb. 22, P3.10 (2015).MathSciNetMATH

12.

LeCompte N., Martin W.J., Owens W.: On the equivalence between real mutually unbiased bases and a certain class of association schemes. Eur. J. Comb. 31, 1499–1512 (2010).MathSciNetCrossRefMATH

13.

Nozaki H., Suda S.: Weighing matrices and spherical codes. J. Algebra Comb. 42, 283–291 (2015).MathSciNetCrossRefMATH

14.

Robinson P.J.: Using product designs to construct orthogonal designs. Bull. Austral Math. Soc. 16, 297–305 (1977).MathSciNetCrossRefMATH

15.

Seberry J., Yamada M.: Hadamard Matrices, Sequences, and Block Designs. Contemporary Design Theory, pp. 431–560. Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley, New York (1992).

16.

Suda S.: A two-fold cover of strongly regular graphs with spreads and association schemes of class five. Des. Codes Cryptogr. 78, 463–471 (2016).MathSciNetCrossRefMATH

17.

van Dam E., Martin W., Muzychuk M.: Uniformity in association schemes and coherent configurations: cometric Q-antipodal schemes and linked systems. J. Comb. Theory Ser. A 120(7), 1401–1439 (2013).MathSciNetCrossRefMATH

18.

Wallis Jennifer Seberry: On the existence of Hadamard matrices. J. Comb. Theory Ser. A 21, 188–195 (1976).MathSciNetCrossRefMATH

19.

Wan Z.: Lectures on Finite Fields and Galois Rings. World Scientific Publishing Co., Inc., River Edge, NJ (2003).CrossRefMATH

Titel: Unbiased orthogonal designs
verfasst von: Hadi Kharaghani
Sho Suda
Publikationsdatum: 16.09.2017
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 7/2018
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-017-0414-9

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Weitere Artikel der Ausgabe 7/2018

On MDS linear complementary dual codes and entanglement-assisted quantum codes

Hermitian rank distance codes

Polynomial-time key recovery attack on the Faure–Loidreau scheme based on Gabidulin codes

New generalized cyclotomic binary sequences of period

Super-strong RKA secure MAC, PKE and SE from tag-based hash proof system

Combinatorial constructions of optimal (m, n, 4, 2) optical orthogonal signature pattern codes