Projective Paley sets

Cossidente, Antonio; Marino, Giuseppe; Pavese, Francesco

doi:10.1002/jcd.21666

“…Projective two-intersection sets (sometimes called two-character sets) are classical configurations from finite geometry that provide a series of constructions [1,2,9,22,24,25,26,27,31,47,54,73] (see also [60,Sect. 9]).…”

Section: Proposition 22 (Fourier Inversion Formula) Let G Be An Abelian Group and Letmentioning

confidence: 99%

“…The construction of partial difference sets is therefore of great interest. We refer to [13,60] for excellent surveys of partial difference sets and equivalent structures, and to [1,2,4,5,8,9,11,12,14,15,17,18,19,20,21,22,24,25,26,27,28,29,30,31,32,37,38,42,43,44,45,46,47,48,49,50,51,52,54,58,59,61,62,63,64,65,67,68,69,…”

Section: Introductionmentioning

confidence: 99%

Packings of partial difference sets

Jedwab¹,

Li²

2021

Combinatorial Theory

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A packing of partial difference sets is a collection of disjoint partial difference sets in a finite group G. This configuration has received considerable attention in design theory, finite geometry, coding theory, and graph theory over many years, although often only implicitly. We consider packings of certain Latin square type partial difference sets in abelian groups having identical parameters, the size of the collection being either the maximum possible or one smaller. We unify and extend numerous previous results in a common framework, recognizing that a particular subgroup reveals important structural information about the packing. Identifying this subgroup allows us to formulate a recursive lifting construction of packings in abelian groups of increasing exponent, as well as a product construction yielding packings in the direct product of the starting groups. We also study packings of certain negative Latin square type partial difference sets of maximum possible size in abelian groups, all but one of which have identical parameters, and show how to produce such collections using packings of Latin square type partial difference sets.

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“…Projective two-intersection sets (sometimes called two-character sets) are classical configurations from finite geometry that provide a series of constructions [1,2,9,22,24,25,26,27,31,47,54,73] (see also [60,Sect. 9]).…”

Section: Historical Overviewmentioning

confidence: 99%

“…The construction of partial difference sets is therefore of great interest. We refer to [13,60] for excellent surveys of partial difference sets and equivalent structures, and to [1,2,4,5,8,9,11,12,14,15,17,18,19,20,21,22,24,25,26,27,28,29,30,31,32,37,38,42,43,44,45,46,47,48,49,50,51,52,54,58,59,61,62,63,64,65,67,68,69,…”

Section: Introductionmentioning

confidence: 99%

Packings of partial difference sets

Jedwab¹,

Li²

2020

Preprint

View full text Add to dashboard Cite

A packing of partial difference sets is a collection of disjoint partial difference sets in a finite group G. This configuration has received considerable attention in design theory, finite geometry, coding theory, and graph theory over many years, although often only implicitly. We consider packings of certain Latin square type partial difference sets in abelian groups having identical parameters, the size of the collection being either the maximum possible or one smaller. We unify and extend numerous previous results in a common framework, recognizing that a particular subgroup reveals important structural information about the packing. Identifying this subgroup allows us to formulate a recursive lifting construction of packings in abelian groups of increasing exponent, as well as a product construction yielding packings in the direct product of the starting groups. We also study packings of certain negative Latin square type partial difference sets of maximum possible size in abelian groups, all but one of which have identical parameters, and show how to produce such collections using packings of Latin square type partial difference sets.

show abstract