LED (AES like) algorithm Decryption-Mixcolumn
The inverse of LED MDS matrix is :

$$\left[
\begin{array}{c c c c}
12 &amp; 12 &amp; 13 &amp; 4 \\
3 &amp; 8 &amp; 4 &amp; 5\\
7 &amp; 6 &amp; 2 &amp; 14\\
13 &amp; 9 &amp; 9 &amp; 13\\
\end{array}\right]$$

you can verify it.

this is sage code that generates the inverse MDS matrix.

f=x^4+x^1+1  # irrudiciable polynomial
L.&lt;z&gt;= GF(2^4,modulus=f)
R=PolynomialRing(L,'x')
N=16
m=[(4,  1, 2, 2),(8,  6, 5, 6),(11,14,10, 9),(2,  2,15,11)]
T= matrix(m)
#print S.inverse()
print m
print T
P=matrix(L,4,4)
P_1=matrix(L,4,4)
for i in range(0,4):
    for j in range(0,4):
        P[i,j]= (T[i][j]) + z^1*(T[i][j]&gt;&gt;1) + z^2*(T[i][j]&gt;&gt;2) + z^3*(T[i][j]&gt;&gt;3)



print P
P_1=P.inverse()
print P_1
# print the matrix with clear distance
for i in range(0,4):
    for j in range(0,4):
        print P_1[i,j]
    print ""