Goppa Codes - Department of Mathematics
Goppa Codes - Department of Mathematics
Goppa Codes - Department of Mathematics
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<strong>Goppa</strong> <strong>Codes</strong> Key One Chung<br />
✬<br />
Now, let’s find points <strong>of</strong> degree 1(rational points) C0(F3).<br />
✫<br />
y 2 − x 3 − 2x − 2 = 0<br />
If x = 0, then y 2 = 2. No such elements in F3.<br />
If x = 1, then y 2 = 2. No such elements in F3.<br />
If x = 2, then y 2 = 2. No such elements in F3.<br />
So, no rational points <strong>of</strong> the type (X : Y : 1).<br />
When Z = 0, −X 3 = 0. So, X = 0.<br />
So, C0(F3) = {P∞ := (0 : 1 : 0)}.<br />
✩<br />
✪<br />
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