Énoncé - L`UTES

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n n ≥1
n D(n)δ n
1≤δ≤n S(n)D(n)
n S(n) = 2n
a b
δ∈D(ab)ab =kδ
d= (a, δ), a =da0, δ =dδ0.
δ0b
ab a
b
ψ D(a)×D(b)
ψ(u, v) = uv ∈N∗
D(ab)
ψ D(a)×D(b)D(ab) (a, b) = 1
(a, b) = 1 S(ab) = S(a)S(b)
p S(p) = p+ 1
k n = 2k−1(2k−1)
2k−1
k= 2,3,4,5,6 7
K=F2[X]/hX4+X3+ 1iα=X
XK
B={1, α, α2, α3}
F2K
K
α5B
αK
a=α5aK∗
a2+a+ 1 = 0
L={0,1, a, a2}K
L={x∈K|x4=x}
L K
L F2K K

G1F2
G1=
1 0 1 0 0 1 1
0 1 1 0 0 0 1
0 0 1 1 1 0 1
1 1 0 0 1 0 1
C1F2G1
C1
C1
C2F2G2
G2=
1 0 1 1 1 0 0
0 1 1 0 1 0 0
0 0 1 0 1 1 1
1 1 0 0 1 0 1
C2
C1C2
H2=
1 0 1 1 1 0 0
1 1 1 0 0 1 0
0 1 1 1 0 0 1
C2
d C2
H2H1C1
m4G11110010
m