Erratum to: “Generalized relative difference sets” (Proc. Amer. Math. Soc. 25 (1970), 46–50) by Payne

Abstract

Abstract. This note gives the correction of a theorem previously published. A counterexample is also given for the theorem as originally stated.In [1], a nonexistence theorem was given for a normal (0, l)-matrix A with three distinct characteristic roots such that A TA = c0I -c,(/m ® /"). However, part (i) of Theorem 1.5 as stated is incorrect. A counterexample is the cyclic relative difference set /?(13, 2, 9, 3) whose elements are (2, 4, 6, 7, 10, 11, 12, 18, 21}. For this set, m is odd and the Hubert symbol (3, 26)3 = -1.