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A new class of near-optimal partial Fourier codebooks from an almost difference set
An ( N , K ) codebook is a set of N unit-norm code vectors in a K -dimensional vector space. Also known as a frame, it has many applications in...
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Construction of rotation symmetric Boolean functions with optimal algebraic immunity and high nonlinearity
Recent research shows that the class of rotation symmetric Boolean functions is potentially rich in functions of cryptographic significance. In this...
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Gauss periods and codebooks from generalized cyclotomic sets of order four
Let p , q be distinct primes with gcd( p − 1, q − 1) = 4. Let D 0 , D 1 , D 2 , D 3 be Whiteman’s generalized cyclotomic classes, satisfying the...
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A new product construction for partial difference sets
Relatively few constructions are known of negative Latin square type Partial Difference Sets (PDSs), and most of the known constructions are in...
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Abelian and non-abelian Paley type group schemes
In this paper, we present a construction of abelian Paley type group schemes which are inequivalent to Paley group schemes. We then determine the...
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Construction of balanced Boolean functions with high nonlinearity and good autocorrelation properties
Boolean functions with high nonlinearity and good autocorrelation properties play an important role in the design of block ciphers and stream...
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Further results on planar DO functions and commutative semifields
It is proven that any Dembowski–Ostrom polynomial is planar if and only if its evaluation map is 2-to-1, which can be used to explain some known...
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Difference sets over Galois rings with odd extension degrees and characteristic an even power of 2
We construct an infinite family of (2 ns , 2 ns /2 -1 (2 ns /2 −1), 2 ns /2 -1 (2 ns /2 -1 −1)) difference sets over a Galois ring GR (2 n , s ) with...
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Construction of cyclotomic codebooks nearly meeting the Welch bound
Ding and Feng (IEEE Trans Inform Theory 52(9):4229–4235,
2006 , IEEE Trans Inform Theory 53(11):4245–4250,2007 ) constructed series of ( N , K )... -
New restrictions on possible orders of circulant Hadamard matrices
We obtain several new number theoretic results which improve the field descent method. We use these results to rule out many of the known open cases...
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Some progress on the existence of 1-rotational Steiner triple systems
A Steiner triple system of order v (briefly STS( v )) is 1-rotational under G if it admits G as an automorphism group acting sharply transitively on...
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A conjecture about binary strings and its applications on constructing Boolean functions with optimal algebraic immunity
In this paper, a combinatorial conjecture about binary strings is proposed. Under the assumption that the proposed conjecture is correct, two classes...
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Geometric and design-theoretic aspects of semibent functions I
The two parts of this paper consider combinatorial and geometric aspects of semibent functions. In the first part of this note we obtain 2-designs...
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The cocyclic Hadamard matrices of order less than 40
In this paper all cocyclic Hadamard matrices of order less than 40 are classified. That is, all such Hadamard matrices are explicitly constructed, up...
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On Lander’s conjecture for difference sets whose order is a power of 2 or 3
Let p be a prime and let b be a positive integer. If a ( v , k , λ , n ) difference set D of order n = p b exists in an abelian group with cyclic Sylow p -s...
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Special subsets of difference sets with particular emphasis on skew Hadamard difference sets
This article introduces a new approach to studying difference sets via their additive properties. We introduce the concept of special subsets, which...
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Wieferich pairs and Barker sequences
We show that if a Barker sequence of length n > 13 exists, then either n = 189 260 468 001 034 441 522 766 781 604, or n > 2 · 10 30 . This improves...
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Paley type partial difference sets in non p-groups
By modifying a construction for Hadamard (Menon) difference sets we construct two infinite families of negative Latin square type partial difference...