How do we calculate the branch number of any given binary matrix?

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Smita Das 2023-5-27

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回答： Srivardhan ，2023-7-6

How do we calculate the hamming weight, branch number of any nxn binary matrix defined in GF(2^n)?

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Answer 1

Srivardhan 2023-7-6

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Hi Smita,

As per my understanding, you want to calculate the branch number and hamming weight of any nxn binary matrix.

In general, Hamming weight of binary matrix is the count of non-zero elements in the matrix. To calculate the branch number of given matrix we need to find absolute maximum in Walsh transform of the matrix. Subtract the maximum absolute value from 2^(n-1) to obtain the branch number.

We can use suitable algorithm to find Walsh transform of the matrix such as Fast Walsh Hadamard transform (FWHT).

Here is the sample code for reference:

function weight = hamming_weight(matrix)
    weight = sum(matrix(:));
end
function bn = branch_number(matrix)
    n = size(matrix, 1);
    transform = fwht(matrix);  % Fast Walsh–Hadamard transform
    abs_transform = abs(transform);
    max_value = max(abs_transform(:));
    bn = 2^(n-1) - floor(max_value);
end
% Example usage
matrix = [1 0 1; 0 1 0; 1 1 1];
weight = hamming_weight(matrix);
bn = branch_number(matrix);
disp(weight); 
disp(bn);