References

References, sorted alphabetically by first author.

A B C D F H J K L M N R S T

A

Ada1997

C. M. Adams. Constructing symmetric ciphers using the cast design procedure. In E. Kranakis and P. Van Oorschot, editors, Selected Areas in Cryptography, 71–104, Boston, MA, (1997). Springer US.

B

BC1999

A. Bernasconi and B. Codenotti. “Spectral analysis of Boolean functions as a graph eigenvalue problem”. IEEE Transactions on Computers, 48(3):345–351, (1999).

BCV2001

A. Bernasconi, B. Codenotti, and J. M. VanderKam. “A characterization of bent functions in terms of strongly regular graphs”. IEEE Transactions on Computers, 50(9):984–985, (2001).

Bos1963

R. C. Bose. “Strongly regular graphs, partial geometries and partially balanced designs”. Pacific J. Math, 13(2):389–419, (1963).

BFFWW2006

I. Bouyukliev, V. Fack, W. Willems, and J. Winne. “Projective two-weight codes with small parameters and their corresponding graphs”. Designs, Codes and Cryptography, 41(1):59–78, (2006).

Bra2006

A. Braeken. Cryptographic Properties of Boolean Functions and S-Boxes. Phd thesis, Katholieke Universiteit Leuven, Leuven-Heverlee, Belgium, (2006).

BCN1989

A. E. Brouwer, A. Cohen, and A. Neumaier. Distance-Regular Graphs. Ergebnisse der Mathematik und Ihrer Grenzgebiete, 3 Folge / A Series of Modern Surveys in Mathematics. Springer London, (2011).

BV1992

A. E. Brouwer and C. A. Van Eijl. “On the p-rank of the adjacency matrices of strongly regular graphs”. Journal of Algebraic Combinatorics, 1(4):329–346, (1992).

C

CalK1986

R. Calderbank and W. M. Kantor. “The geometry of two-weight codes”. Bulletin of the London Mathematical Society, 18(2):97–122, (1986).

Car2010

C. Carlet. Boolean functions for cryptography and error correcting codes. In Boolean Models and Methods in Mathematics, Computer Science, and Engineering, volume 2, 257–397. Cambridge University Press, (2010).

CDPS2010

C. Carlet, L. E. Danielsen, M. G. Parker, and P. Solé. “Self-dual bent functions”. International Journal of Information and Coding Theory, 1(4):384–399, (2010).

CTZ2011

Y. M. Chee, Y. Tan, and X. D. Zhang. “Strongly regular graphs constructed from p-ary bent functions”. Journal of Algebraic Combinatorics, 34(2):251–266, (2011).

D

Del1972

P. Delsarte. “Weights of linear codes and strongly regular normed spaces”. Discrete Mathematics, 3(1-3):47–64, (1972).

Dil1974

J. F. Dillon. Elementary Hadamard Difference Sets. PhD thesis, University of Maryland College Park, Ann Arbor, USA, (1974).

DS1987

J. F. Dillon and J. R. Schatz. “Block designs with the symmetric difference property”. In Proceedings of the NSA Mathematical Sciences Meetings, 159–164. US Govt. Printing Office Washington, DC, (1987).

Din2015

C. Ding. “Linear codes from some 2-designs”. IEEE Transactions on information theory, 61(6):3265–3275, (2015).

DD2015

K. Ding and C. Ding. “A class of two-weight and three-weight codes and their applications in secret sharing”. IEEE Transactions on Information Theory, 61(11):5835–5842, (2015).

F

FSSW2013

T. Feulner, L. Sok, P. Solé, and A. Wassermann. “Towards the classification of self-dual bent functions in eight variables”. Designs, Codes and Cryptography, 68(1):395–406, (2013).

H

HL1994

C. Hoede and X. Li. “Clique polynomials and independent set polynomials of graphs”. Discrete Mathematics, 125(1):219 – 228, (1994).

HY2004

T. Huang and K.-H. You. “Strongly regular graphs associated with bent functions”. In 7th International Symposium on Parallel Architectures, Algorithms and Networks, 2004. Proceedings, 380–383, May 2004.

J

JGTMMBJP2013

D. Joyner, O. Geil, C. Thomsen, C. Munuera, I. Márquez-Corbella, E. Martínez-Moro, M. Bras-Amorós, R. Jurrius, and R. Pellikaan. “Sage: A basic overview for coding theory and cryptography.” In Algebraic Geometry Modeling in Information Theory, volume 8 of Series on Coding Theory and Cryptology, 1–45. World Scientific Publishing Company, (2013).

JK2007

T. Junttila and P. Kaski. “Engineering an efficient canonical labeling tool for large and sparse graphs”. In D. Applegate, G. S. Brodal, D. Panario, and R. Sedgewick, editors, Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments and the Fourth Workshop on Analytic Algorithms and Combinatorics, 135–149, New Orleans, LA, (2007). Society for Industrial and Applied Mathematics.

JK2011

T. Junttila and P. Kaski. “Conflict propagation and component recursion for canonical labeling”. In Theory and Practice of Algorithms in (Computer) Systems, 151–162. Springer, (2011).

K

Kan1975

W. M. Kantor. “Symplectic groups, symmetric designs, and line ovals”. Journal of Algebra, 33(1):43–58, (1975).

Kan1983

W. M. Kantor. “Exponential numbers of two-weight codes, difference sets and symmetric designs”. Discrete Mathematics, 46(1):95–98, (1983).

L

Lan2010

P. Langevin. “Classification of partial spread functions in eight variables”, (2010). http://langevin.univ-tln.fr/project/spread/psp.html Last accessed 9 May 2017.

LH2011

P. Langevin and X.-D. Hou. “Counting partial spread functions in eight variables”. IEEE Transactions on Information Theory, 57(4):2263–2269, (2011).

LL2011

P. Langevin and G. Leander. “Counting all bent functions in dimension eight 99270589265934370305785861242880.” Designs, Codes and Cryptography, 59(1-3):193–205, (2011).

LLM2008

P. Langevin, G. Leander, and G. McGuire. Kasami bent functions are not equivalent to their duals. In G. Mullen, D. Panario, and I. Shparlinski, editors, Finite Fields and Applications: Eighth International Conference on Finite Fields and Applications, July 9-13, 2007, Melbourne, Australia, Contemporary mathematics, 187–198. American Mathematical Society, (2008).

Leo2016GitHub

P. Leopardi. Boolean-cayley-graphs, (2016). https://github.com/penguian/Boolean-Cayley-graphs GitHub repository. Last accessed 9 May 2017.

Leo2016SMC

P. Leopardi. Boolean-cayley-graphs, (2016). http://tinyurl.com/Boolean-Cayley-graphs SageMathCloud public folder. Last accessed 9 May 2017.

Leo2017Hurwitz

P. Leopardi. “Twin bent functions, strongly regular Cayley graphs, and Hurwitz-Radon theory”. Submitted October 2016 to Journal of Algebra Combinatorics Discrete Structures and Applications, accepted April 2017. Preprint: arXiv:1504.02827 [math.CO].

Leo2017

P. Leopardi. “Classifying bent functions by their Cayley graphs”. 2017, 2018. Preprint: arXiv:1705.04507 [math.CO].

M

MP2013

B. D. McKay and A. Piperno. Nauty and Traces user’s guide (Version 2.5). Computer Science Department, Australian National University, Canberra, Australia, (2013).

MP2014

B. D. McKay and A. Piperno. “Practical graph isomorphism, II”. Journal of Symbolic Computation, 60:94–112, (2014).

MS1990

W. Meier and O. Staffelbach. “Nonlinearity criteria for cryptographic functions”. In J.-J. Quisquater and J. Vandewalle, editors, Advances in Cryptology — EUROCRYPT ‘89: Workshop on the Theory and Application of Cryptographic Techniques, volume 434 of Lecture Notes in Computer Science, 549–562, Berlin, Heidelberg, (1990). Springer.

N

Neu2006

T. Neumann. Bent functions. PhD thesis, University of Kaiserslautern, (2006).

R

RFC2144

C. M. Adams. The cast-128 encryption algorithm. RFC 2144, RFC Editor, May 1997.

Rot1976

O. S. Rothaus. “On ‘bent’ functions”. Journal of Combinatorial Theory, Series A, 20(3):300–305, (1976).

Roy2008

G. F. Royle. “A normal non-cayley-invariant graph for the elementary abelian group of order 64”. Journal of the Australian Mathematical Society, 85(03):347–351, (2008).

S

SageMathCloud

SageMath, Inc. SageMathCloud Online Computational Mathematics, (2016). https://cloud.sagemath.com

Sei1979

J. J. Seidel. “Strongly regular graphs”. In Surveys in combinatorics (Proc. Seventh British Combinatorial Conf., Cambridge, 1979), volume 38 of London Mathematical Society Lecture Note Series, 157–180, Cambridge-New York, (1979). Cambridge Univ. Press.

Sta2007

P. Stanica. “Graph eigenvalues and Walsh spectrum of Boolean functions”. Integers: Electronic Journal Of Combinatorial Number Theory, 7(2):A32, (2007).

Sti2007

D. R. Stinson. Combinatorial designs: constructions and analysis. Springer Science & Business Media, (2007).

SageMath7517

The Sage Developers. SageMath, the Sage Mathematics Software System (Version 7.5), (2017). http://www.sagemath.org

T

Tok2015

N. Tokareva. Bent functions: results and applications to cryptography. Academic Press, (2015).

Ton1996

V. D. Tonchev. “The uniformly packed binary [27, 21, 3] and [35, 29, 3] codes”. Discrete Mathematics, 149(1-3):283–288, (1996).

Ton2007

V. D. Tonchev. “Codes”. In C. Colbourne and J. Dinitz, editors, Handbook of combinatorial designs, chapter VII.1, 677–701. CRC press, second edition, (2007).