The problem involves finding all solutions to a system of equations in the binary field Z2. The equations presented are linear and include variables x1, x2, x3, x4, and x5, with the goal of determining the total number of solutions.
Some participants have provided guidance on the nature of the system and the expected form of the equations after reduction. There is an ongoing exploration of the implications of the reduced equations and how to enumerate possible solutions based on variable combinations.
Participants note the importance of working within the constraints of Z2, where certain operations may yield different results compared to standard arithmetic. There is also mention of the need to evaluate combinations of specific variables to find all solutions.
vela said:The presence of a 1 on the RHS isn't a problem. You're trying to solve an inhomogeneous system, so a constant term in the solution is expected.
What equations did you get after you reduced them?
Mark44 said:Since this is a nonhomogeneous system (as vela points out), you should be working with an augmented matrix with 3 rows and 6 columns. The sixth column will have the constants.