How to solve the code}

How to find GF(2^m)

clc;
clear all;
close all;

x1='1100110011';
x2='1111001100';
y0='0000000000';
H ='1111011010'

yy= xor(y0-'0',x1-'0');
y1=gfmul(yy,H);

I got an error as this: Error using gfmul All inputs must be real integers.

Error in hash1 (line 11) y1=gfmul(yy,H);

What correction should i make?

[KSSV]

Read the doc here: https://in.mathworks.com/help/comm/ref/gfmul.html gfmul accepts double i.e matrix as input. You are inputting a string and logical which is not correct.

Answer 1

[Guillaume]

It's not very clear what exactly you're intending to gfmul. If it's the two numbers that are represented by the binary pattern in yy and H (one being a vector of bits, the other a char array of bits), then maybe:

x1 = '1100110011';
x2 = '1111001100';
y0 = '0000000000';
H = '1111011010';

yy = xor(y0-'0',x1-'0');

y1 = gfmul(polyval(yy, 2), bin2dec(H));

polyval(b, 2) converts a vector of bits into the corresponding decimal value. bin2dec(s) converts a char array of bits into the corresponding decimal value. And as you already know, b = s - '0' (and s = char(b + '0')).

[Darsana P M]

Now the error is: Error using gfmul The input elements must be binary.

Is it because of the input? Actually the input when i check in command window is yy =

Columns 1 through 9

     1     1     0     0     1     1     0     0     1

Column 10

     1

And x1 =

1100110011

So the inputs are still different. What change must be done?

[Darsana P M]

Actually now i understood the problem, in the above code:

clc;
clear all;
close all;
x1={'1' '1' '0' '0' '1' '1' '0' '0' '1' '1'};
X=cell2mat(x1);
x2={'0' '0' '0' '0' '0' '0' '0' '0' '0' '0'};
XX=cell2mat(x2);
yy= xor(X-'0',XX-'1');
y1 = gfconv(yy, [1 1 1 1 0 1 1 0 1 0],2);

In this line: y1 = gfconv(yy, [1 1 1 1 0 1 1 0 1 0],2); Now i get an error, saying the inputs arenot binary. But if I provide a matrix in place of yy as[1 0 1] y1 = gfconv([1 0 1], [1 1 1 1 0 1 1 0 1 0],2); Now i get an output.

But now my problem is, i want the XORed value to be given as input in gfconv() What should I do?

[Guillaume]

xor is a logical operator and hence return logical arrays. Converting that to double should resolve your problem (I don't have the comms toolbox):

y1 = gfconv(double(yy), [1 1 1 1 0 1 1 0 1 0],2);

Note that the doc says that if p is 2, you can use the normal operations conv and .*.

[Darsana P M]

Yes now its correct. Thanks a lot.

Answer 2

[Walter Roberson]

y1 = gfmul(yy, bin2dec(H));

[Darsana P M]

Thanks. The above error mentioned s not there. But now the error is: Error using gfmul The inputs must have the same size and orientation.

Error in hash1 (line 11) y1 = gfmul(yy, bin2dec(H));

clc;
clear all;
close all;

x1='1100110011';
x2='1111001100';
y0='0000000000';
H ='1111011010'

yy= xor(y0-'0',x1-'0');
y1 = gfmul(yy, bin2dec(H));

[Walter Roberson]

gfmul needs three inputs, the third of which describes the galois field.