Note on a Question by S. Bagchi and B. Bagchi

نویسنده

  • Bernhard Schmidt
چکیده

In [l] Bagchi and Bagchi conjectured that one of the hypotheses of their theorem 2(d) is superfluous. This turns out to be true: PROPOSITION. Let 4 = 9 mod 16 be a prime power such that 2 is a fourth power in Fq. Then 1 f fi are nonsquares in Fp. Pruc$ Let p be a primitive eighth root of unity in Fq (note that /3 is a nonsquare). Because of (02 + 1)2 = p4 + 202 + 1 = 202 we obtain that (0 * + 1)/p is a root of 2 which we denote by fi. Note that fi is a square and therefore p* + 1 is a nonsquare. Thus the equation (1 + Q/3@* + 1) = (02 + p + l)@ + 1) = p(1 + p)* shows that 1 + fi is a nonsquare in Fq. Since (1 + @(l fi) = -1 this is also true for 1 4%.

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عنوان ژورنال:
  • Des. Codes Cryptography

دوره 2  شماره 

صفحات  -

تاریخ انتشار 1992