I already know how the set of solutions of system of linear equations over real numbers infinite field is expressed.
When there is only single solution then it is just a vector of scalars, where each scalar is a real number.
When there are more than 1 solution, and actually infinite solutions, then it is just a parametric linear vector space in the form: where where n denotes the number of real variables in each linear equation thus
But my question is how the set of solutions of system of linear equations over the finite field or galois field GF(2) is expressed?
I already know that when there is only single solution then it is also just a vector of scalars, but where each scalar is a binary number either zero or one in where , but when there are more than 1 solution, but always finite number of solutions, then how are they expressed?
Is this similar to how real solutions are expressed by parametric linear vector space by modulo 2? Or something else? I don't know. I am trying to google the answer for this question for days but I don't find the answer anywhere. It seems like nobody talks about this topic.