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Title: New partial difference sets in ℤt p 2 and a related problem about Galois rings
Authors: Hou, X.-D.
Leung, K.H. 
Xiang, Q.
Keywords: Finite field
Galois ring
Partial difference set
Teichmüller set
The Cauchy-Davenport theorem
The Dyson e-transform
Issue Date: Jan-2001
Citation: Hou, X.-D., Leung, K.H., Xiang, Q. (2001-01). New partial difference sets in ℤt p 2 and a related problem about Galois rings. Finite Fields and their Applications 7 (1) : 165-188. ScholarBank@NUS Repository.
Abstract: We generalize a construction of partial difference sets (PDS) by Chen, Ray-Chaudhuri, and Xiang through a study of the Teichmüller sets of the Galois rings. Let R=GR(p2, t) be the Galois ring of characteristic p2 and rank t with Teichmüller set T and let π:R→R/pR be the natural homomorphism. We give a construction of PDS in R with the parameters ν=p2t, k=r(pt-1), λ=pt+r2-3r, μ=r2-r, where r=lpt-s(p, t), 1≤l≤ps(p, t), and s(p, t) is the largest dimension of a GF(p)-subspace W⊂R/pR such that π-1(W)∩T generates a subgroup of R of rank
Source Title: Finite Fields and their Applications
ISSN: 10715797
DOI: 10.1006/ffta.2000.0307
Appears in Collections:Staff Publications

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