I am working with Galois field. I obtained all the 256 values, and now i want to make the matrix form of the obtained values.

Question

Muhammad Zeeshan Khan 2023-8-29

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2014281-i-am-working-with-galois-field-i-obtained-all-the-256-values-and-now-i-want-to-make-the-matrix-for

评论： Voss 2023-8-30

clear all;
close all;
clc;
m = 8;    
p = 2;
prim_poly = p^8+p^6+p^5+p^1+p^0;       
a = gf(35, m, prim_poly);      
b = gf(15, m, prim_poly);       
c = gf(0, m, prim_poly);        
d = gf(5, m, prim_poly);        
x_gf = gf([a b; c d] , m , prim_poly);
determinant = det(gf(x_gf, m, prim_poly));
% Check singularity
if determinant == 0
    disp('The linear fractional transformation is singular.');
else
    disp('The linear fractional transformation is not singular.');
end
%s = zeros(1,256);
for x_gf = 0:255
    e = conv(a, x_gf);
    f = conv(c, x_gf);
    h = e + b; 
    j = f + d; 
    i = gf(1./j, m, prim_poly);
    results = gf(conv(h, i),m, prim_poly)
end   

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Answer 1

Fangjun Jiang 2023-8-30

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2014281-i-am-working-with-galois-field-i-obtained-all-the-256-values-and-now-i-want-to-make-the-matrix-for#answer_1297611

在 MATLAB Online 中打开

results = zeros(1,256);
for x_gf = 0:255
    e = conv(a, x_gf);
    f = conv(c, x_gf);
    h = e + b; 
    j = f + d; 
    i = gf(1./j, m, prim_poly);
    results(x_gf+1) = gf(conv(h, i),m, prim_poly)
end   

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Voss 2023-8-30

在 MATLAB Online 中打开

clear all;
close all;
clc;
m = 8;    
p = 2;
prim_poly = p^8+p^6+p^5+p^1+p^0;       
a = gf(35, m, prim_poly);      
b = gf(15, m, prim_poly);       
c = gf(0, m, prim_poly);        
d = gf(5, m, prim_poly);        
x_gf = gf([a b; c d] , m , prim_poly);
determinant = det(gf(x_gf, m, prim_poly));
Warning: Lookup tables not defined for this order 2^8 and
primitive polynomial 355.  Arithmetic still works
correctly but multiplication, exponentiation, and
inversion of elements is faster with lookup tables.
Use gftable to create and save the lookup tables.
% Check singularity
if determinant == 0
    disp('The linear fractional transformation is singular.');
else
    disp('The linear fractional transformation is not singular.');
end
The linear fractional transformation is not singular.
%s = zeros(1,256);
results = zeros(1,256);
for x_gf = 0:255
    e = conv(a, x_gf);
    f = conv(c, x_gf);
    h = e + b; 
    j = f + d; 
    i = gf(1./j, m, prim_poly);
    results(x_gf+1) = gf(conv(h, i),m, prim_poly)
end
Unable to perform assignment because value of type 'gf' is not convertible to 'double'.

Caused by:
    Error using double
    Conversion to double from gf is not possible.

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Answer 2

Voss 2023-8-30

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2014281-i-am-working-with-galois-field-i-obtained-all-the-256-values-and-now-i-want-to-make-the-matrix-for#answer_1297631

在 MATLAB Online 中打开

clear all;
close all;
clc;
m = 8;    
p = 2;
prim_poly = p^8+p^6+p^5+p^1+p^0;       
a = gf(35, m, prim_poly);      
b = gf(15, m, prim_poly);       
c = gf(0, m, prim_poly);        
d = gf(5, m, prim_poly);        
x_gf = gf([a b; c d] , m , prim_poly);
determinant = det(gf(x_gf, m, prim_poly));
Warning: Lookup tables not defined for this order 2^8 and
primitive polynomial 355.  Arithmetic still works
correctly but multiplication, exponentiation, and
inversion of elements is faster with lookup tables.
Use gftable to create and save the lookup tables.
% Check singularity
if determinant == 0
    disp('The linear fractional transformation is singular.');
else
    disp('The linear fractional transformation is not singular.');
end
The linear fractional transformation is not singular.
%s = zeros(1,256);
results = cell(1,256);
for x_gf = 0:255
    e = conv(a, x_gf);
    f = conv(c, x_gf);
    h = e + b;
    j = f + d;
    i = gf(1./j, m, prim_poly);
    results{x_gf+1} = gf(conv(h, i),m, prim_poly);
end
disp(results);
  Columns 1 through 16

    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}

  Columns 17 through 32

    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}

  Columns 33 through 48

    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}

  Columns 49 through 64

    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}

  Columns 65 through 80

    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}

  Columns 81 through 96

    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}

  Columns 97 through 112

    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}

  Columns 113 through 128

    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}

  Columns 129 through 144

    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}

  Columns 145 through 160

    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}

  Columns 161 through 176

    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}

  Columns 177 through 192

    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}

  Columns 193 through 208

    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}

  Columns 209 through 224

    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}

  Columns 225 through 240

    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}

  Columns 241 through 256

    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}    {1×1 gf}
results{1}
 
ans = GF(2^8) array. Primitive polynomial = D^8+D^6+D^5+D+1 (355 decimal)
 
Array elements = 
 
   3
results{2}
 
ans = GF(2^8) array. Primitive polynomial = D^8+D^6+D^5+D+1 (355 decimal)
 
Array elements = 
 
   67