On the diophantine equation y2 = 4qn + 4q + 1

Abstract

It is known that a certain class of [n, k] codes over GF(q) is related to the diophantine equation y2 = 4qn + 4q + 1 (*). In Parts I and II of this paper, two different, and in a certain sense complementary, methods of approach to (*) are discussed and some results concerning (*) are given as applications. A typical result is that the only solutions to (*) are (y, n) = (5, 1), (7, 2), (11, 3) when q = 3 and (y, n) = (2q + 1, 2) when q = 3f, f >- 2. © 1986.