Using Constraint Solvers to Construct Binary Codes with Good Error Correction Performance

In recent years, constraint solvers show increasing use in solving various open combinatorial problems, e.g., from Ramsey theory or synthesis of combinatorial designs. The similar approach can be applied to some problems related to binary linear codes, which form one of the largest families of error correcting codes used both in coding theory and in various practical applications. Thanks to a simple algebraic structure of such codes it is possible to study them using a wide range of methods. Note that even codes with the same basic parameters (length n, dimension k, minimum code distance d) can show different error correction performance, i.e., the ability to correct errors which appear in a noisy channel. In the paper, we formulate the problem of finding binary linear codes with good error correction performance as a constraint optimization problem and explore the effectiveness of modern constraint solvers on it, including SAT, MaxSAT, and CP solvers. Using the respective solvers and parallel computing, for several values of n, k, d we found the codes which are significantly better than the known in terms of their practical performance.