We often use *linear equations* in coding theory, although the ring/field may vary significantly. If the linear code has no redundancy, the set of equations has exactly one solution, which presumably can be found via Gaussian elimination. If the linear code has redundancy, then the system of equations is overdetermined, and only has a solution if the code hasn't been corrupted. All of the cleverness of ECC codes boils down to how to determine the *maximum likelihood* solution. Now in a field of characteristic 0 -- e.g., R or C -- we have the method of *least squares* to find solutions to sets of overdetermined equations. Are any of the standard ECC methods for other fields -- e.g., various Galois fields -- *equivalent to a least squares* method of solution? I.e., if Ax=b is the overdetermined system, and A' is the Hermitian conjugate transpose of A, are the x's found by solving (A'A)x=(A'b) the same as those computed by any other ECC schemes? What if we "lift" the original equation set Ax=b from one field into another, larger field?