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1. More translation planes and semifields from Dembowski–Ostrom polynomials

   In this article we use pairs of Dembowski–Ostrom polynomials with special properties (see (P1)–(P3) in the introduction below) to construct...

   Ulrich Dempwolff in Designs, Codes and Cryptography

   Article 27 June 2012

2. Nonfactorizable nonsingular hypercubes

   We investigate nonsingular hypercubes, and prove several results, stating a condition for a hypercube to be the product of hypercubes of smaller...

   David G. Glynn in Designs, Codes and Cryptography

   Article 19 November 2011

3. Finite semifields and nonsingular tensors

   In this article, we give an overview of the classification results in the theory of finite semifields (note that this is not intended as a survey of...

   Michel Lavrauw in Designs, Codes and Cryptography

   Article 14 June 2012

4. Planes in which every quadrangle lies on a unique Baer subplane

   Desarguesian projective planes of square order are characterized by the property that every quadrangle lies on a unique Baer subplane.

   William M. Kantor, Tim Penttila in Designs, Codes and Cryptography

   Article 24 September 2011

5. The existence of maximal (q ², 2)-arcs in projective Hjelmslev planes over chain rings of length 2 and odd prime characteristic

   We prove that ( q ² , 2)-arcs exist in the projective Hjelmslev plane PHG(2, R ) over a chain ring R of length 2, order | R | =  q ² and prime...

   Thomas Honold, Michael Kiermaier in Designs, Codes and Cryptography

   Article 07 April 2012

6. 42-arcs in PG(2, q) left invariant by PSL(2, 7)

   Lucia Indaco, Gábor Korchmáros in Designs, Codes and Cryptography

   Article 18 June 2011

7. Commutative semifields from projection map**s

   We describe a general projection method to construct commutative semifields in odd characteristic. One application yields a family of commutative...

   Jürgen Bierbrauer in Designs, Codes and Cryptography

   Article 04 November 2010

8. Polarities and unitals in the Coulter–Matthews planes

   For a class of finite shift planes introduced by Coulter and Matthews, we give a set of representatives for the isomorphism types, determine all...

   Norbert Knarr, Markus Stroppel in Designs, Codes and Cryptography

   Article 17 September 2009

9. Uniqueness of some cyclic projective planes

   Yiwei Huang, Bernhard Schmidt in Designs, Codes and Cryptography

   Article 28 August 2008

10. Further translation planes of order 19² admitting SL(2,5), obtained by nest replacement

    We construct three translation planes of order 19 ² admitting SL(2,5), obtained by replacement of 24-nests of reguli in PG(3,19).

    Alan R. Prince in Designs, Codes and Cryptography

    Article 18 April 2008

11. On the Ree Unital

    Alessandro Montinaro in Designs, Codes and Cryptography

    Article 13 December 2007

12. A nearfield-free definition of regular Hughes planes and some embeddings of PG(3,q) in Hughes planes of order q ⁴

    We give a nearfield-free definition of some finite and infinite incidence systems by means of half-points and half-lines and show that they are...

    Julia M. N. Brown in Designs, Codes and Cryptography

    Article 11 August 2007

13. On the Hughes–Kleinfeld and Knuth’s semifields two-dimensional over a weak nucleus

    In 1960 Hughes and Kleinfeld (Am J Math 82:389–392, 1960) constructed a finite semifield which is two-dimensional over a weak nucleus, given an...

    Simeon Ball, Michel Lavrauw in Designs, Codes and Cryptography

    Article 26 April 2007

14. On 2 – (n ², 2n, 2n–1) designs with three intersection numbers

    Andrea Caggegi, Giovanni Falcone in Designs, Codes and Cryptography

    Article 23 March 2007

15. A translation plane of order 19² admitting SL(2,5), obtained by 12-nest replacement

    The problem of determining two-dimensional translation planes admitting SL(2,5) in the translation complement has been intensively studied. Most...

    Alan R. Prince in Designs, Codes and Cryptography

    Article 20 March 2007

16. Projective aspects of the AES inversion

    We consider the nonlinear function used in the Advanced Encryption Standard (AES). This nonlinear function is essentially inversion in the finite...

    Wen-Ai Jackson, S. Murphy in Designs, Codes and Cryptography

    Article 18 May 2007

17. Sublines of Prime Order Contained in the Set of Internal Points of a Conic

    In [2] it was shown that if q ≥ 4 n ² −8 n +2 then there are no subplanes of order q contained in the set of internal points of a conic in PG(2, q ^...

    Michel Lavrauw in Designs, Codes and Cryptography

    Article 01 January 2006

18. Eigenvalues of Finite Projective Planes with an Abelian Cartesian Group

    Let M be an incidence matrix for a projective plane of order n . The eigenvalues of M are calculated in the Desarguesian case and a standard form for M ...

    J. L. Hayden in Designs, Codes and Cryptography

    Article 01 September 2004

19. Planar Oval Sets in Desarguesian Planes of Even Order

    A planar oval set in PG (2, q ), q even, is a set of q ² ovals in PG (2, q ) with common nucleus which intersect pairwise in one point. We classify...

    Nikias de Feyter in Designs, Codes and Cryptography

    Article 01 May 2004

20. On a Class of Symmetric Balanced Generalized Weighing Matrices

    Let q be a prime power and m a positive integer. A construction method is given to “multiply” the parametrs of an ω-circulant BGW(v=1+q+q ₂ +·+ q ^...

    H. Kharaghani in Designs, Codes and Cryptography

    Article 01 September 2003