I have a Diophantine system Ax=b and Cx<=d where A and C are m*n matrices that I want to solve subject to the constraint that x consists of integers that are between 0 and k (inclusive). Looking through the documentation centre I have found the following tutorial regarding Diophantine polynomial systems (https://reference.wolfram.com/language/tutorial/DiophantineReduce.html) which uses the reduce function to solve the system. This works perfectly other than the fact that each equation and inequality must be entered separately, and I need to perform this for large systems. Ideally I would like to be able to call the function with the matrices directly, along the lines of

Reduce[A*x == b && C*x <= d && 0 <= x <= k, x, Integers]

to return all possible solutions for x. Is this possible with reduce, or any other function? Keeping in mind that I need all solutions to be returned. As a side note, I know that there are solutions to my system. Thanks.