Conjecture 3 For p [equivalent to] 1 (mod 4), the associated QQR code and its dual satisfy: [C.
The following well-known result (v) shall be used to estimate the weights of codewords of QQR codes.
Goppa's conjecture implies that the minimum distance of our QQR code with rate R = 1/2 satisfies d < [[delta].
This, and the fact that R = 1/2 for our QQR codes (with p [equivalent to] 1 (mod 4)), imply [delta] [less than or equal to] [[delta].
Using SAGE, it can be shown that the Riemann hypothesis is not valid for these "extended QQR codes" in general, as the following example illustrates.