The input elements must be integers between -Inf and P^M-2 over an extension field

I am working on a Galois field (2 ^ 4) which means that I am manipulating data whose values ​​are between 0 and 15 (2 ^ 4-1). but when I build my Galois field using the instruction field = gftuple ([- 1: 2 ^ m-2] ', m, 2); when I want to add in two vectors on my Galois field using gfadd (a, b, field), if one of the vectors contains the value 15 the operation is not performed and the message that is displayed is ''The input elements must be integers between -Inf and P ^ M-2 over an extension field.'' however 15 is an element of my Galois field

m = 4          %Determine the Galois Field, GF(2^m)
n = 2^m-1    %This is fixed for a Reed-Solomon, the length of the codeword
k = 3          %The number of data symbols, can be anything between 1 to n - 1
h = n-k
t = h/2

field = gftuple([-1:2^m-2]', m, 2);

Answer 1

[Walter Roberson]

https://www.mathworks.com/help/comm/ref/gftuple.html

Exponential is assumed for column vectors.

For exponential the limit is not 2^m-2 and is instead 2^(m-2)

[Kevin Ntako]

sorry I do not understand your last sentence!

why does 15 in a vector produce an error despite the fact that it belongs to the Galois field (2 ^ 4)? is there any other way to build my Galois field to make it work?

thank you for helping me!

[Walter Roberson]

You used a column vector of values. When you do that, the input is not gf members, and instead is exponents. Negative exponents correspond to gf member 0. The maximum exponent is m-2.

If you want your input to be gf members then you need a row instead of a column and you would not use negative entries.