How to Find the Covering Radius of Linear Codes over Finite Fields Using a Parity-Check Matrix in Parallel

We present a parallel algorithm for computing the covering radius of a linear [n, k]q code using its parity-check matrix. The method is based on the systematic generation of syndromes associated with linear combinations of columns of the parity-check matrix. To improve scalability, the search space is partitioned and processed in parallel using a master–worker strategy implemented with the Message Passing Interface (MPI). The proposed approach significantly reduces the computational effort required for covering radius computation, a problem known to be NP-hard in general. Experimental results demonstrate that the parallelization achieves substantial speedups and makes the exact computation of the covering radius feasible for codes of larger parameters.