If we consider GF(8) as a vector space over GF(2), what are the basis for GF(8)? and How can we define a dual space for GF(8) as a vector space?
2026-03-30 05:25:25.1774848325
Basis of finite field as vector space
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Since GF(8) is the polynomial ring over GF(2) modulo some irreducible cubic polynomial $p(x)$ over GF(2), you can just take the monomials $1$, $x$, $x^2$ for a basis. Surely, from this you can work out the dual space, by taking linear combinations of coefficients of polynomials representing elements of GF(8)?