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
VL - 362
SP - 2189
EP - 2204
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 4
ER -