16. The system of claim 10 , wherein the collapsing includes multiplying a matrix times the solution.
10. A memory system comprising: a memory including memory cells and constraints on symbol values stored in the memory cells; and an encoder in communication with the memory, the encoder configured for: receiving write data to be encoded into a write word that satisfies the constraints on the symbol values; encoding the write data into the write word, the encoding comprising: representing the write data and the constraints as a first linear system in a first field of a first size; embedding the first linear system into a second linear system in a second field of a second size, the second size larger than the first size; solving the second linear system in the second field resulting in a solution; and collapsing the solution into the first field resulting in the write word, the write word satisfying the constraints on symbol values in the write word; and transmitting the write word to the memory.