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This article is cited in 1 scientific paper (total in 1 paper)
Goppa codes on a family of algebraic number fields
M. M. Glukhov (jr.)
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.
Received: 26.06.2000
Citation:
M. M. Glukhov (jr.), “Goppa codes on a family of algebraic number fields”, Diskr. Mat., 13:2 (2001), 14–34; Discrete Math. Appl., 11:3 (2001), 213–234
Linking options:
https://www.mathnet.ru/eng/dm281https://doi.org/10.4213/dm281 https://www.mathnet.ru/eng/dm/v13/i2/p14
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