How to perform reduced row echelon form on a non-square GF matrix (GF(2^8)) in matlab

Question

%GF(2^8)

m=8
mat1  = gf([160 28 233 185 176],8);
result1 = gf([160 28 233 185 176],8)/gf([160],8)    
% 1          77         174          32         220
[R,jb] = rref([1 77 174 32 220;189 244 80 245 190])

I use the result from result1 as 1st row and progressively add the next row vector [189 244 80 245 190]

% reduced row echelon
mat2 = [1 77 174 32 220;189 244 80 245 190]
a = gf([1 77 174 32 220;189 244 80 245 190],8); 
r2 = a(2,:); r1 = gf(189,8) * a(1,:); 
subt = r2 -r1; a(2,:)= subt./gf(122,8); 
a(1,:) = a(1,:)- (gf(77,8) *a(2,:)); 
disp(a) 

mat3 = [[1 0 101 105 110]; [0 1 163 128 97]; [157 233 247 64 118]];
m3 = gf(mat3,8); 
m3(3,:)= m3(3,:) - (gf(157,8) * m3(1,:)) 
m3(3,:)= m3(3,:) - (gf(233,8) * m3(2,:))
m3(3,:)= m3(3,:)./ gf(29,8) .

rref works without GF(2^8). But I am unable to perform the reduction using GF(2^8) . Can someone help me to find a solution and how to proceed? I will be using the result from the above and append another row-vector to the it. Is there any function we can solve it, instead of going step-by-step

What is `G(2^8)` meant to do at the start of this code? What do you mean by "using G(2^8)"? — Wolfie, Jun 22 '22 at 14:15
G is Galois Field (typo error), it's only for the description, corrected it GF(2^8). The code starts from the field value which is m=8. — Beneyaz Ara Begum, Jun 23 '22 at 04:54

How to perform reduced row echelon form on a non-square GF matrix (GF(2^8)) in matlab

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