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Question: Galois Field 2^m with polynomial rank less than m

Question:Galois Field 2^m with polynomial rank less than m

Maldark 5 Maple 2018
October 11 2018
1

I am currently implementing the math behind the McEliece Cryptosystem in Maple, and as such I need to do work in the Galois Field GF(2^m). In my working example I am working with p=2, k=4, and a=1+x (i.e. the rank of my polynomial is 1). Parameters are per documentation found at https://www.maplesoft.com/support/help/maple/view.aspx?path=GF.

 

When attempting to initialize this field, however, I am receiving an error that the rank is not 4=k as expected. It is, however, not a requirement for a field that the polynomial has to be of rank k. How do I go about this?

G16 := GF(2, 4, 1+x);
Error, (in GF) polynomial 1+x does not determine an extension of degree 4
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