This is the accepted version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published inACM Transactions on Mathematical Software. Volume 49, Issue 1, https://doi.org/10.1145/3573383The minimum distance of a linear code is a key concept in information theory. Therefore, the time required by its computation is very important to many problems in this area. In this article, we introduce a family of implementations of the Brouwer–Zimmermann algorithm for distributed-memory architectures for computing the minimum distance of a random linear code over 2. Both current commercial and public-domain software only work on either unicore architectures or shared-memory architectures, which are limited in the number of cores/processors employed in the computation. Our implementations focus on distributed-memory architectures, thus being able to employ hundreds or even thousands of cores in the computation of the minimum distance. Our experimental results show that our implementations are much faster, even up to several orders of magnitude, than current implementations widely used nowadays.The authors would like to thank the University of Alicante for granting access to the ua cluster. They also want to thank Javier Navarrete for his assistance and support when working on this machine. The authors would also like to thank Robert A. van de Geijn from the University of Texas at Austin for granting access to the skx cluster.Quintana-Ortí was supported by the Spanish Ministry of Science, Innovation and Universities under Grant RTI2018-098156-B-C54 co-financed by FEDER funds.
Hernando was supported by the Spanish Ministry of Science, Innovation and Universities under Grants PGC2018-096446-B-C21 and PGC2018-096446-B-C22, and by University Jaume I under Grant PB1-1B2018-10.
Igual was supported by Grants PID2021-126576NB-I00 and RTI2018-B-I00, funded by MCIN/AEI/10.13039/501100011033
and by “ERDF A way of making Europe”, and the Spanish CM (S2018/TCS-4423). This work has been supported by the Madrid Government (Comunidad de Madrid, Spain) under the Multiannual Agreement with Complutense University in the line Program to Stimulate Research for Young Doctors in the context of the V PRICIT (Regional Programme of Research and Technological Innovation) under project PR65-19/22445
