Geodesic
Goppa codes on a family of algebraic number fields
Diskretnaya Matematika, Tome 13 (2001) no. 2, pp. 14-34.

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We describe some properties of the geometric Goppa codes on the curve determined by the equation $$ y^s=(x^{q^{(n-u)/2}-1}+1)^a (x^{q^{(n+u)/2}-1}+1)^b $$ over a finite field $K=F_{q^n}$ with an arbitrary odd $q$, $n>1$, where $s=a+b$, $s\mid q-1$, $u=1$ for odd $n$ and $u=2$ for even $n$. We find the number of the $F_{q^n}$-rational points of the curve and the degrees and ramification indexes of the maximal ideals of the discrete valuation rings of the field $K(x,y)$. In some cases, the bases of the codes are found. 
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M. M. Glukhov (jr.). Goppa codes on a family of algebraic number fields. Diskretnaya Matematika, Tome 13 (2001) no. 2, pp. 14-34. http://geodesic.mathdoc.fr/item/DM_2001_13_2_a1/

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