TY - JOUR

T1 - Sets with integral distances in finite fields

AU - Iosevich, Alex

AU - Shparlinski, Igor E.

AU - Xiong, Maosheng

N1 - Copyright 2009 American Mathematical Society. First published in Transactions of the American Mathematical Society, 362(4), 2189-2204, published by the American Mathematical Society. The original article can be found at http://dx.doi.org/10.1090/S0002-9947-09-05004-1

PY - 2010/4

Y1 - 2010/4

N2 - Given a positive integer n, a finite field Fq of q elements (q odd), and a non-degenerate quadratic form Q on Fqn, in this paper we study the largest possible cardinality of subsets ε⊆ Fqn with pairwise integral Q-dis- tances; that is, for any two vectors × = (xi,⋯,xn),y = (yi,.,yn) ∞εA,one has Q(x - y) = u2 for some u ∞ F q.

AB - Given a positive integer n, a finite field Fq of q elements (q odd), and a non-degenerate quadratic form Q on Fqn, in this paper we study the largest possible cardinality of subsets ε⊆ Fqn with pairwise integral Q-dis- tances; that is, for any two vectors × = (xi,⋯,xn),y = (yi,.,yn) ∞εA,one has Q(x - y) = u2 for some u ∞ F q.

UR - http://www.scopus.com/inward/record.url?scp=77950899257&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-09-05004-1

DO - 10.1090/S0002-9947-09-05004-1

M3 - Article

AN - SCOPUS:77950899257

SN - 0002-9947

VL - 362

SP - 2189

EP - 2204

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 4

ER -