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x^1+1 - primitive
x^2+x^1+1 - primitive
x^3+x^1+1 - primitive
x^3+x^2+1 - primitive
x^4+x^1+1 - primitive
x^4+x^3+1 - primitive
x^4+x^3+x^2+x^1+1 - irreducible
x^5+x^2+1 - primitive
x^5+x^3+1 - primitive
x^5+x^3+x^2+x^1+1 - primitive
x^5+x^4+x^2+x^1+1 - primitive
x^5+x^4+x^3+x^1+1 - primitive
x^5+x^4+x^3+x^2+1 - primitive
x^6+x^1+1 - primitive
x^6+x^3+1 - irreducible
x^6+x^4+x^2+x^1+1 - irreducible
x^6+x^4+x^3+x^1+1 - primitive
x^6+x^5+1 - primitive
x^6+x^5+x^2+x^1+1 - primitive
x^6+x^5+x^3+x^2+1 - primitive
x^6+x^5+x^4+x^1+1 - primitive
x^6+x^5+x^4+x^2+1 - irreducible
x^7+x^1+1 - primitive
x^7+x^3+1 - primitive
x^7+x^3+x^2+x^1+1 - primitive
x^7+x^4+1 - primitive
x^7+x^4+x^3+x^2+1 - primitive
x^7+x^5+x^2+x^1+1 - primitive
x^7+x^5+x^3+x^1+1 - primitive
x^7+x^5+x^4+x^3+1 - primitive
x^7+x^5+x^4+x^3+x^2+x^1+1 - primitive
x^7+x^6+1 - primitive
x^7+x^6+x^3+x^1+1 - primitive
x^7+x^6+x^4+x^1+1 - primitive
x^7+x^6+x^4+x^2+1 - primitive
x^7+x^6+x^5+x^2+1 - primitive
x^7+x^6+x^5+x^3+x^2+x^1+1 - primitive
x^7+x^6+x^5+x^4+1 - primitive
x^7+x^6+x^5+x^4+x^2+x^1+1 - primitive
x^7+x^6+x^5+x^4+x^3+x^2+1 - primitive
x^8+x^4+x^3+x^1+1 - irreducible
x^8+x^4+x^3+x^2+1 - primitive
x^8+x^5+x^3+x^1+1 - primitive
x^8+x^5+x^3+x^2+1 - primitive
x^8+x^5+x^4+x^3+1 - irreducible
x^8+x^5+x^4+x^3+x^2+x^1+1 - irreducible
x^8+x^6+x^3+x^2+1 - primitive
x^8+x^6+x^4+x^3+x^2+x^1+1 - primitive
x^8+x^6+x^5+x^1+1 - primitive
x^8+x^6+x^5+x^2+1 - primitive
x^8+x^6+x^5+x^3+1 - primitive
x^8+x^6+x^5+x^4+1 - primitive
x^8+x^6+x^5+x^4+x^2+x^1+1 - irreducible
x^8+x^6+x^5+x^4+x^3+x^1+1 - irreducible
x^8+x^7+x^2+x^1+1 - primitive
x^8+x^7+x^3+x^1+1 - irreducible
x^8+x^7+x^3+x^2+1 - primitive
x^8+x^7+x^4+x^3+x^2+x^1+1 - irreducible
x^8+x^7+x^5+x^1+1 - irreducible
x^8+x^7+x^5+x^3+1 - primitive
x^8+x^7+x^5+x^4+1 - irreducible
x^8+x^7+x^5+x^4+x^3+x^2+1 - irreducible
x^8+x^7+x^6+x^1+1 - primitive
x^8+x^7+x^6+x^3+x^2+x^1+1 - primitive
x^8+x^7+x^6+x^4+x^2+x^1+1 - irreducible
x^8+x^7+x^6+x^4+x^3+x^2+1 - irreducible
x^8+x^7+x^6+x^5+x^2+x^1+1 - primitive
x^8+x^7+x^6+x^5+x^4+x^1+1 - irreducible
x^8+x^7+x^6+x^5+x^4+x^2+1 - primitive
x^8+x^7+x^6+x^5+x^4+x^3+1 - irreducible
Скрипт
clc;
clear;
N=8;
ck=1;
for n=2:2^(N+1)-1
k=n;
for m=N:-1:0
if k>=2^m
k=k-2^m;
a(n,N+1-m)=1;
else
a(n,N+1-m)=0;
end
end
endfor cnt=2:2^(N+1)-1
if (a(cnt,N+1)) % for speed
clear poly;
z=0;
for c=1:N+1
if (~z && a(cnt,c))
z=1;
end
if (z)
poly(z)=a(cnt,c);
z=z+1;
end
enda_gf = gf(poly,1);
is_reducible = 0;
for n=2:2^floor(log2(cnt))-1
clear poly;
z=0;
for c=1:N+1
if (~z && a(n,c))
z=1;
end
if (z)
poly(z)=a(n,c);
z=z+1;
end
end
b_gf = gf(poly,1);
[q,r]=deconv(a_gf,b_gf);
if (isempty(find(r.x))) % all elements are zeros
is_reducible = 1;
end
end
if (~is_reducible)
flg=0;
for m=1:N+1
if (a(cnt,m))
if (flg)
fprintf(1,'+');
end
flg=1;
if (m~=N+1)
fprintf(1,'x^%u',N+1-m);
else
fprintf(1,'1',N+1-m);
end
end
end
if (isprimitive(a_gf))
fprintf(1,' - primitive');
else
fprintf(1,' - irreducible');
end
fprintf(1,'\n');
end
end
end
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