Abstract:
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.