Note on the dimension of Goppa codes
Let Γ ( L , g ) be a Goppa code over F q , where L ⊂ F q m is a support and g ( x ) ∈ F q m [ x ] is a polynomial with s distinct roots in F q m . In [Couvreur A, Otmani A, Tillich JP (2014) New identities relating wild Goppa codes. Finite Field Appl 29: 178–197.], Couvreur at al. gave the bound: di...
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| Veröffentlicht in: | Applicable algebra in engineering, communication and computing communication and computing, 2024-09, Vol.35 (5), p.683-690 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let
Γ
(
L
,
g
)
be a Goppa code over
F
q
, where
L
⊂
F
q
m
is a support and
g
(
x
)
∈
F
q
m
[
x
]
is a polynomial with
s
distinct roots in
F
q
m
. In [Couvreur A, Otmani A, Tillich JP (2014) New identities relating wild Goppa codes. Finite Field Appl 29: 178–197.], Couvreur at al. gave the bound:
dim
F
q
Γ
(
L
,
g
e
)
-
dim
F
q
Γ
(
L
,
g
e
+
1
)
≤
s
,
where
e
=
q
m
-
1
+
q
m
-
2
+
⋯
+
q
. In this paper, we give the conditions such that
dim
F
q
Γ
(
L
,
g
e
)
=
dim
F
q
Γ
(
L
,
g
e
+
1
)
. |
|---|---|
| ISSN: | 0938-1279 1432-0622 |
| DOI: | 10.1007/s00200-022-00578-z |