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All Two-Weight Irreducible Cyclic Codes?
The aim of this paper is the classification of two-weight irreducible cyclic codes. Using Fourier transforms and Gauss sums, we obtain necessary and sufficient numerical conditions for an irreducibleExpand
Cyclotomic integers and finite geometry
The most powerful method for the study of finite geometries with regular or quasiregular automorphism groups G is to translate their definition into an equation over the integral group ring 2[G] andExpand
The Field Descent Method
TLDR
Applications include the verification of Lander’s conjecture for all difference sets whose order is a power of a prime >3 and for all McFarland, Spence and Chen/Davis/Jedwab difference sets. Expand
Proof of the prime power conjecture for projective planes of order $n$ with Abelian collineation groups of order $n^2$
Let G be an abelian collineation group of order n 2 of a projective plane of order n. We show that n must be a prime power, and that the p-rank of G is at least b + 1 if n = p b for an odd prime p.
Williamson Matrices and a Conjecture of Ito's
  • Bernhard Schmidt
  • Mathematics, Computer Science
  • Des. Codes Cryptogr.
  • 1 September 1999
TLDR
It is shown that there are relative difference sets in the dicyclic groups Q8t of the form t = 2a · 10b · 26c · m with a, b, c ≥ 0, m ≡ 1\ (mod 2), which gives further support to an important conjecture of Ito IT5 which asserts thatthere are relative (4t, 2, 4T, 2t)-difference sets in Q8T for every positive integer t. Expand
Characters and Cyclotomic Fields in Finite Geometry
1. Introduction: The nature of the problems.- The combinatorial structures in question.- Group rings, characters, Fourier analysis.- Number theoretic tools.- Algebraic-combinatorial tools. 2. TheExpand
New restrictions on possible orders of circulant Hadamard matrices
TLDR
This work uses several new number theoretic results to rule out many of the known open cases of the circulant Hadamard matrix conjecture and settles the only known open case of the Barker sequence conjecture. Expand
Geometry, Combinatorial Designs and Related Structures: Difference sets: an update
In the last few years there has been rapid progress in the theory of difference sets. This is a survey of these fascinating new developments.
On ...-Relative Difference Sets
Towards Ryser’s Conjecture
Ryser’s conjecture asserts that there is no (v, k, λ) -difference set with gcd(v, k − λ) > 1 in any cyclic group. We survey what is known on this conjecture and obtain progress towards it byExpand
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