New partial difference sets in ℤt p 2 and a related problem about Galois rings

Please use this identifier to cite or link to this item: https://doi.org/10.1006/ffta.2000.0307

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. https://doi.org/10.1006/ffta.2000.0307
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
URI:	http://scholarbank.nus.edu.sg/handle/10635/103603
ISSN:	10715797
DOI:	10.1006/ffta.2000.0307
Appears in Collections:	Staff Publications

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