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Nested Hadamard Difference Sets, James A. Davis, Jonathan Jedwab
Nested Hadamard Difference Sets, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
A Hadamard difference set (HDS) has the parameters (4N2, 2N2 − N, N2 − N). In the abelian case it is equivalent to a perfect binary array, which is a multidimensional matrix with elements ±1 such that all out-of-phase periodic autocorrelation coefficients are zero. We show that if a group of the form H × Z2pr contains a (hp2r, √hpr(2√hpr − 1), √hpr(√hpr − 1)) HDS (HDS), p a prime not dividing |H| …
Partial Difference Sets In P-Groups, James A. Davis
Partial Difference Sets In P-Groups, James A. Davis
Department of Math & Statistics Faculty Publications
Most of the examples of PDS have come in p-groups, and most of these examples are in elementary abelian p-groups. In this paper, we will show an exponent bound for PDS with the same parameters as the elementary abelian case.
Rely To "Comment On 'Nonexistence Of Certain Perfect Binary Arrays' And 'Nonexistence Of Perfect Binary Arrays'", Jonathan Jedwab, James A. Davis
Rely To "Comment On 'Nonexistence Of Certain Perfect Binary Arrays' And 'Nonexistence Of Perfect Binary Arrays'", Jonathan Jedwab, James A. Davis
Department of Math & Statistics Faculty Publications
Yang's comment [C] is based on a lemma which claims to construct an s0 x s1 x s2 x ... x s, perfect binary array (PBA) from an s0s1 x s2 x ... x sr PBA.
Nonexistence Of Certain Perfect Binary Arrays, Jonathan Jedwab, James A. Davis
Nonexistence Of Certain Perfect Binary Arrays, Jonathan Jedwab, James A. Davis
Department of Math & Statistics Faculty Publications
A perfect binary array (PBA) is an r-dimensional matrix with elements ±I such that all out-of-phase periodic autocorrelation coefficients are zero. The two smallest sizes for which the existence of a PBA is undecided, 2 x 2 x 3 x 3 x 9 and 4 x 3 x 3 x 9, are ruled out using computer search and a combinatorial argument.
A Summary Of Menon Difference Sets, James A. Davis, Jonathan Jedwab
A Summary Of Menon Difference Sets, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
A (v, k, λ) difference set is a k-element subset D of a group G of order v for which the multiset {d1d2-1 : d1,d2 ∈ D, d1 ≠ d2} contains each nonidentity element of G exactly λ times. A difference set is called abelian, nonabelian or cyclic if the underlying group is. Difference sets a.re important in design theory because they a.re equivalent to symmetric (v, k, λ) designs with a regular automorphism group. Abelian difference sets arise naturally in …