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+# A Delsarte Bound calculator in MATLAB
+
+The `delsarte(n, d)` function returns an upper bound for $A_2(n, d)$: the maximum number of binary code-words of length $n$ and having Hamming distance $d$ between each other.
+
+The obtained bound can often be improved (see [this table](https://www.win.tue.nl/~aeb/codes/binary-1.html)), with further observations and only for special cases, but this function can compute a valid bound for any value of $n$ and $d$.

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+function r = comb(n, k)
+    r = gamma(n + 1) / (gamma(k + 1) * gamma(n - k + 1)); 
+end

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+function r = delsarte(n, d)
+    % https://www.win.tue.nl/~aeb/codes/binary-1.html
+
+    if d > n
+        r = 1;
+        return
+    end
+
+    if 1.5 * d > n
+        r = 2;
+        return
+    end
+    
+    m = n - d + 1;
+
+    % populate the objective function
+    c = -ones(1, m);
+    
+    A = zeros(n, m);
+    b = zeros(1, n);
+    for t = 1:n
+        % populate the A matrix
+        for j = 1:m
+            i = n - m + j;
+            A(t, j) = - k(t, n, i);
+        end
+        % populate the b vector
+        b(1, t) = k(t, n, 0);
+    end
+
+    % populate non-negativity constraints
+    lb = zeros(1, m);
+    
+    % fill other parameters
+    Aeq = [];
+    beq = [];
+
+    % find an optimal solution
+    s = sym(linprog(c, A, b, Aeq, beq, lb));
+
+    % add the value of x_0 and round the result
+    r = fix(sum(s) + 1);
+end

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+function r = k(t, n, i)
+    r = 0;
+    for j = 0:min(i, t)
+        r = r + ((-1)^j * comb(i, j) * comb(n - i, t - j));
+    end
+end