Publications of Bernhard Schmidt
Books
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Characters and Cyclotomic Fields in Finite Geometry.
Lecture Notes in Mathematics 1797, Springer 2002.
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Differenzmengen und relative Differenzmengen.
Doctoral dissertation. Verlag Dr. Wissner, Augsburg 1995.
Papers
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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).
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Unique sums and differences in finite Abelian groups.
J. Number Theory
233 (2022), 370-388
(with K. H. Leung).
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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).
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Upper Bounds for Cyclotomic Numbers.
Algebraic Combinatorics 3 (2020), 39-53.
(with T. D. Duc and K. H. Leung).
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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.
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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).
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Nonexistence Results on Generalized Bent Functions
(Z q ) m -> Zq
with Odd m and q = 2 mod 4.
J. Comb. Theory Ser. A
163 (2019), 1-33.
(with K. H. Leung).
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Structure of Group Invariant Weighing Matrices of Small Weight.
J. Comb. Theory Ser. A
154 (2018), 114-128
(with K. H. Leung).
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Unique Differences in Symmetric Subsets of Fp.
Combinatorica
37 (2017), 167-182
(with T. D. Duc).
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A Survey of the Multiplier Conjecture.
Des. Codes Cryptogr.
78 (2016), 221-236
(with D. M. Gordon).
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The Anti-Field-Descent Method.
J. Comb. Theory Ser. A
139 (2016), 87-131
(with K. H. Leung).
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A Multiplier Theorem.
J. Comb. Theory Ser. A
124 (2014), 228-243
(with K. H. Leung and S. L. Ma).
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Hadamard Difference Sets Related to Lander's Conjecture.
J. Algebra
403 (2014), 29-47
(with T. Feng, K. H. Leung, and K. W. Smith).
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Construction of Relative Difference Sets and
Hadamard Groups.
Des. Codes Cryptogr. 73
(2014), 105-119
(with M. M. Tan).
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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).
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New Restrictions on Possible Orders of Circulant Hadamard Matrices.
Des. Codes Cryptogr.
64 (2012), 143-151
(with K. H. Leung).
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Finiteness of Circulant Weighing Matrices of Fixed Weight.
J. Comb. Theory Ser. A
118 (2011), 908-919
(with K. H. Leung).
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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).
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Fast Computation of Gauss Sums and Resolution of the
Root of Unity Ambiguity.
Acta Arith.
140 (2009), 205-232
(with D. K. Nguyen).
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Uniqueness of Some Cyclic Projective Planes.
Des. Codes Cryptogr.
50 (2009), 253-266
(with Y. Huang).
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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).
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Finite Fourier Series and Ovals in PG(2,2h).
J. Aust. Math. Soc.
81 (2006), 21-34
(with C. J. Fisher).
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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).
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The Field Descent Method.
Des. Codes Cryptogr.
36 (2005), 171-188
(with K. H. Leung).
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The field descent and class groups of CM-fields.
Acta Arith. 119 (2005), 291-306.
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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).
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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).
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Asymptotic nonexistence of difference sets in dihedral groups.
J. Combin. Theory Ser. A
99 (2002), 261-280 (with K. H. Leung).
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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).
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All Two-Weight Irreducible Cyclic Codes?
Finite Fields Appl. 8 (2002), 1-17
(with C. White).
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Bijections between Group Rings Preserving Character Sums.
Des. Codes Cryptogr. 24 (2001), 243-254
(with M. Hagita).
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Exponent Bounds.
Finite Geometries. Proceedings of the Forth Isle of Thorns Conference.
Eds. A. Blokhuis et. al.,
Kluwer Academic Publishers 2001, 319-331.
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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).
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Towards Ryser's Conjecture.
Proc. 3rd European Congress of Mathematics. Eds. C. Casacuberta et al.,
Progress in Mathematics 201 , Birkhäuser 2001, 533-541.
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Relative (pa,pb,pa,pb-a)-difference sets:
A Unified Exponent Bound and a Local Ring Construction.
Finite Fields Appl. 6 (2000), 1-22 (with S. L. Ma).
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Williamson Matrices and a Conjecture of Ito's.
Des. Codes Cryptogr. 17 (1999), 61-68.
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Cyclotomic Integers and Finite Geometry.
J. Am. Math. Soc. 12 (1999), 929-952.
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Difference Sets: A Second Update.
Rend. Circ. Palermo Serie II, Suppl.
53 (1998), 89-118 (with D. Jungnickel).
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Cyclotomic Integers of Prescribed Absolute Value and the Class Group.
J. Number Theory
72 (1998), 269-281.
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Nonexistence Results on Chen and Davis-Jedwab Difference Sets.
J. Algebra 202 (1998), 404-413.
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Nonexistence of a (783,69,6)-difference set.
Discrete Math. 178 (1998), 283-285.
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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).
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Difference Sets Corresponding to a Class of Symmetric
Designs.
Des. Codes and Crypt.
10 (1997), 223-236 (with S. L. Ma).
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A Sharp Exponent Bound for McFarland Difference Sets
with p=2.
J. Combin. Theory Ser. A
80 (1997), 347-352 (with S. L. Ma).
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A multiplier theorem for projections of affine difference
sets.
J. Stat. Plann. Inf.
62 (1997), 63-67
(with A. Pott and D. Reuschling).
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On (pa,pb,pa,pa-b)-Relative
Difference Sets.
J. Alg. Combin. 6 (1997), 279-297.
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On (pa,p,pa,pa-1)-Relative Difference Sets.
Des. Codes and Crypt. 6 (1995), 57-71
(with S. L. Ma).
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The Structure of Abelian Groups Containing McFarland
Difference Sets.
J. Combin. Theory Ser. A
70 (1995), 313-322
(with S. L. Ma).
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A Note on a Question of R. Baghi and S. Baghi.
Des. Codes and Crypt. 2 (1992), 395.