Publications of Bernhard Schmidt

Books

• Characters and Cyclotomic Fields in Finite Geometry.
  Lecture Notes in Mathematics 1797, Springer 2002.
  


• Differenzmengen und relative Differenzmengen.
  Doctoral dissertation. Verlag Dr. Wissner, Augsburg 1995.

Papers

• On the nonexistence of semi-regular relative difference sets.
  J. Comb. Theory Ser. A, to appear, 30 pp. (with K. H. Leung and T. Zhang).
  


• Unique sums and differences in finite Abelian groups.
  J. Number Theory 233 (2022), 370-388 (with K. H. Leung).
  


• Constructions of Butson Hadamard matrices invariant under Abelian p-groups.
  J. Comb. Theory Ser. A 181 (2021), Paper No. 105433, 23 pp. (with Q. Wong and Q. Xiang).
  


• Upper Bounds for Cyclotomic Numbers.
  Algebraic Combinatorics 3 (2020), 39-53. (with T. D. Duc and K. H. Leung).
  


• A Survey of Group Invariant Butson Matrices and Their Relation to Generalized Bent Functions and Various Other Objects.
  Radon Series on Computational and Applied Mathematics 23 (2019), 241-251.
  


• Bilinear Forms on Finite Abelian Groups and Group Invariant Butson Hadamard Matrices.
  J. Comb. Theory Ser. A 166 (2019), 337-351. (with T. D. Duc).
  


• Nonexistence Results on Generalized Bent Functions (Z _q ) ^m -> Z_q with Odd m and q = 2 mod 4.
  J. Comb. Theory Ser. A 163 (2019), 1-33. (with K. H. Leung).
  


• Structure of Group Invariant Weighing Matrices of Small Weight.
  J. Comb. Theory Ser. A 154 (2018), 114-128 (with K. H. Leung).
  


• Unique Differences in Symmetric Subsets of F_p.
  Combinatorica 37 (2017), 167-182 (with T. D. Duc).
  


• A Survey of the Multiplier Conjecture.
  Des. Codes Cryptogr. 78 (2016), 221-236 (with D. M. Gordon).
  


• The Anti-Field-Descent Method.
  J. Comb. Theory Ser. A 139 (2016), 87-131 (with K. H. Leung).
  


• A Multiplier Theorem.
  J. Comb. Theory Ser. A 124 (2014), 228-243 (with K. H. Leung and S. L. Ma).
  


• Hadamard Difference Sets Related to Lander's Conjecture.
  J. Algebra 403 (2014), 29-47 (with T. Feng, K. H. Leung, and K. W. Smith).
  


• Construction of Relative Difference Sets and Hadamard Groups.
  Des. Codes Cryptogr. 73 (2014), 105-119 (with M. M. Tan).
  


• Circulant Weighing Matrices Whose Order and Weight are Products of Powers of 2 and 3.
  J. Comb. Theory Ser. A 120 (2013), 274-287 (with K. W. Smith).
  


• New Restrictions on Possible Orders of Circulant Hadamard Matrices.
  Des. Codes Cryptogr. 64 (2012), 143-151 (with K. H. Leung).
  


• Finiteness of Circulant Weighing Matrices of Fixed Weight.
  J. Comb. Theory Ser. A 118 (2011), 908-919 (with K. H. Leung).
  


• On Lander's conjecture for Difference Sets whose Order is a Power of 2 or 3.
  Des. Codes Cryptogr. 56 (2010), 79-84 (with K. H. Leung and S. L. Ma).
  


• Fast Computation of Gauss Sums and Resolution of the Root of Unity Ambiguity.
  Acta Arith. 140 (2009), 205-232 (with D. K. Nguyen).
  


• Uniqueness of Some Cyclic Projective Planes.
  Des. Codes Cryptogr. 50 (2009), 253-266 (with Y. Huang).
  


• Proper partial geometries with Singer groups and pseudogeometric partial difference sets.
  J. Combin. Theory A 115 (2008), 147-177 (with K. H. Leung and S. L. Ma).
  


• Finite Fourier Series and Ovals in PG(2,2^h).
  J. Aust. Math. Soc. 81 (2006), 21-34 (with C. J. Fisher).
  


• New Hadamard Matrices of Order 4p² obtained from Jacobi Sums of Order 16.
  J. Combin. Theory Ser. A (2006), 822-838 (with K. H. Leung and S. L. Ma).
  


• The Field Descent Method.
  Des. Codes Cryptogr. 36 (2005), 171-188 (with K. H. Leung).
  


• The field descent and class groups of CM-fields.
  Acta Arith. 119 (2005), 291-306.
  


• Nonexistence of abelian difference sets: Lander's conjecture for prime power orders.
  Trans. Amer. Math. Soc. 356 (2004), 4343-4358 (with K. H. Leung and S. L. Ma).
  


• Constructions of Relative Difference Sets with Classical Parameters and Circulant Weighing Matrices.
  J. Combin. Theory Ser. A 99 (2002), 111-127 (with K. H. Leung and S. L. Ma).
  


• Asymptotic nonexistence of difference sets in dihedral groups.
  J. Combin. Theory Ser. A 99 (2002), 261-280 (with K. H. Leung).
  


• Proof of the prime power conjecture for projective planes of order n with abelian collineation groups of order n².
  Proc. Amer. Math. Soc. 130 (2002), 1473-1476 (with A. Blokhuis und D. Jungnickel).
  


• All Two-Weight Irreducible Cyclic Codes?
  Finite Fields Appl. 8 (2002), 1-17 (with C. White).
  


• Bijections between Group Rings Preserving Character Sums.
  Des. Codes Cryptogr. 24 (2001), 243-254 (with M. Hagita).
  


• Exponent Bounds.
  Finite Geometries. Proceedings of the Forth Isle of Thorns Conference. Eds. A. Blokhuis et. al.,
  Kluwer Academic Publishers 2001, 319-331.
  


• On a class of symmetric divisible designs which are almost projective planes.
  Finite Geometries. Proceedings of the Forth Isle of Thorns Conference. Eds. A. Blokhuis et. al.,
  Kluwer Academic Publishers 2001, 27-34 (with A. Blokhuis and D. Jungnickel).
  


• Towards Ryser's Conjecture.
  Proc. 3rd European Congress of Mathematics. Eds. C. Casacuberta et al.,
  Progress in Mathematics 201 , Birkhäuser 2001, 533-541.
  


• Relative (p^a,p^b,p^a,p^b-a)-difference sets: A Unified Exponent Bound and a Local Ring Construction.
  Finite Fields Appl. 6 (2000), 1-22 (with S. L. Ma).
  


• Williamson Matrices and a Conjecture of Ito's.
  Des. Codes Cryptogr. 17 (1999), 61-68.
  


• Cyclotomic Integers and Finite Geometry.
  J. Am. Math. Soc. 12 (1999), 929-952.
  


• Difference Sets: A Second Update.
  Rend. Circ. Palermo Serie II, Suppl. 53 (1998), 89-118 (with D. Jungnickel).
  


• Cyclotomic Integers of Prescribed Absolute Value and the Class Group.
  J. Number Theory  72 (1998), 269-281.
  


• Nonexistence Results on Chen and Davis-Jedwab Difference Sets.
  J. Algebra 202 (1998), 404-413.
  


• Nonexistence of a (783,69,6)-difference set.
  Discrete Math. 178 (1998), 283-285.
  


• Difference Sets: An Update.
  In: Geometry, Combinatorial Designs and Related Structures. Proc. First Pythagorean Conf., Eds. J.W.P. Hirschfeld et. al.
  Cambridge University Press (1997), 89-112 (with D. Jungnickel).
  


• Difference Sets Corresponding to a Class of Symmetric Designs.
  Des. Codes and Crypt. 10 (1997), 223-236 (with S. L. Ma).
  


• A Sharp Exponent Bound for McFarland Difference Sets with p=2.
  J. Combin. Theory Ser. A 80 (1997), 347-352 (with S. L. Ma).
  


• A multiplier theorem for projections of affine difference sets.
  J. Stat. Plann. Inf. 62 (1997), 63-67 (with A. Pott and D. Reuschling).
  


• On (p^a,p^b,p^a,p^a-b)-Relative Difference Sets.
  J. Alg. Combin. 6 (1997), 279-297.
  


• On (p^a,p,p^a,p^a-1)-Relative Difference Sets.
  Des. Codes and Crypt. 6 (1995), 57-71 (with S. L. Ma).
  


• The Structure of Abelian Groups Containing McFarland Difference Sets.
  J. Combin. Theory Ser. A 70 (1995), 313-322 (with S. L. Ma).
  


• A Note on a Question of R. Baghi and S. Baghi.
  Des. Codes and Crypt. 2 (1992), 395.