{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T00:40:14Z","timestamp":1774485614533,"version":"3.50.1"},"reference-count":26,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2019,6,5]],"date-time":"2019-06-05T00:00:00Z","timestamp":1559692800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"Spanish Ministry of Economy","award":["MTM2012-36917-C03-03 and MTM2015-65764-C3-2-P"],"award-info":[{"award-number":["MTM2012-36917-C03-03 and MTM2015-65764-C3-2-P"]}]},{"name":"EU (FEDER) and the Spanish MINECO","award":["TIN 2015-65277-R and TIN2012-32180"],"award-info":[{"award-number":["TIN 2015-65277-R and TIN2012-32180"]}]},{"name":"University Jaume I","award":["P1.1B2015-02"],"award-info":[{"award-number":["P1.1B2015-02"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2019,6,30]]},"abstract":"<jats:p>\n            The minimum distance of an error-correcting code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is crucial to many problems in this area. In this article, we present and assess a family of implementations of both the brute-force algorithm and the Brouwer-Zimmermann algorithm for computing the minimum distance of a random linear code over F\n            <jats:sub>2<\/jats:sub>\n            that are faster than current implementations, both in the commercial and public domain. In addition to the basic sequential implementations, we present parallel and vectorized implementations that produce high performances on modern architectures. The attained performance results show the benefits of the developed optimized algorithms, which obtain remarkable improvements compared with state-of-the-art implementations widely used nowadays.\n          <\/jats:p>","DOI":"10.1145\/3302389","type":"journal-article","created":{"date-parts":[[2019,6,6]],"date-time":"2019-06-06T12:28:42Z","timestamp":1559824122000},"page":"1-28","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":12,"title":["Algorithm 994"],"prefix":"10.1145","volume":"45","author":[{"given":"Fernando","family":"Hernando","sequence":"first","affiliation":[{"name":"Universidad Jaume I, Castell\u00f3 (Spain)"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francisco D.","family":"Igual","sequence":"additional","affiliation":[{"name":"Universidad Complutense de Madrid, Madrid (Spain)"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gregorio","family":"Quintana-Ort\u00ed","sequence":"additional","affiliation":[{"name":"Universidad Jaume I, Castell\u00f3 (Spain)"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2019,6,5]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1976.1055578"},{"key":"e_1_2_2_2_1","first-page":"12","article-title":"GUAVA, a GAP package for computing with error-correcting codes","volume":"3","author":"Baart R.","year":"2012","journal-title":"Version"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1978.1055873"},{"key":"e_1_2_2_4_1","unstructured":"OpenMP Architecture Review Board. 2008. OpenMP Application Program Interface Version 3.0. Retrieved from http:\/\/www.openmp.org\/mp-documents\/spec30.pdf.  OpenMP Architecture Review Board. 2008. OpenMP Application Program Interface Version 3.0. Retrieved from http:\/\/www.openmp.org\/mp-documents\/spec30.pdf."},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1996.0125"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2014.2345375"},{"key":"e_1_2_2_7_1","volume-title":"Discovering Mathematics with Magma. Algorithms Comput. Math.","author":"Grassl Markus"},{"key":"e_1_2_2_8_1","unstructured":"M. Grassl. 2007. Bounds on the minimum distance of linear codes. Retrieved from http:\/\/www.codetables.de.  M. Grassl. 2007. Bounds on the minimum distance of linear codes. Retrieved from http:\/\/www.codetables.de."},{"issue":"7","key":"e_1_2_2_9_1","first-page":"8","article-title":"GAP\u2014Groups, Algorithms, and Programming","volume":"4","author":"The GAP Group","year":"2015","journal-title":"Version"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2010.2095170"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.3934\/amc.2010.4.363"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1983.1056621"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2002.807285"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICDCS.2007.99"},{"key":"e_1_2_2_16_1","doi-asserted-by":"crossref","unstructured":"Petr Lisonek and Layla Trummer. 2015. An Extension of the Brouwer-Zimmermann Minimum Weight Algorithm. 255--262.  Petr Lisonek and Layla Trummer. 2015. An Extension of the Brouwer-Zimmermann Minimum Weight Algorithm. 255--262.","DOI":"10.1007\/978-3-319-17296-5_27"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1109\/LCOMM.2002.804244"},{"key":"e_1_2_2_18_1","volume-title":"North-Holland Mathematical Library","volume":"16","author":"MacWilliams F. J.","year":"1977"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/358746.358762"},{"key":"e_1_2_2_20_1","volume-title":"Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP\u201911)","author":"Nazir S."},{"key":"e_1_2_2_21_1","first-page":"159","article-title":"Knapsack-type cryptosystems and algebraic coding theory","volume":"15","author":"Niederreiter H.","year":"1986","journal-title":"Problems Control Inform. Theory\/Problemy Upravlen. Teor. Inform."},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/359168.359176"},{"key":"e_1_2_2_23_1","volume-title":"Proceedings of the 81st IEEE Vehicular Technology Conference (VTC Spring\u201915)","author":"Sipos M."},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1109\/18.641542"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2016.7541753"},{"key":"e_1_2_2_26_1","volume-title":"Proceedings of the 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks. 1--7.","author":"Zhang Xiaolan"},{"key":"e_1_2_2_27_1","unstructured":"K. H. Zimmermann. 1996. Integral Hecke Modules Integral Generalized Reed-Muller Codes and Linear Codes. Techn. Univ. Hamburg-Harburg. Retrieved from https:\/\/books.google.es\/books?id&equals;_2FamwEACAAJ.  K. H. Zimmermann. 1996. Integral Hecke Modules Integral Generalized Reed-Muller Codes and Linear Codes. Techn. Univ. Hamburg-Harburg. Retrieved from https:\/\/books.google.es\/books?id&equals;_2FamwEACAAJ."}],"container-title":["ACM Transactions on Mathematical Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3302389","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3302389","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T01:01:48Z","timestamp":1750208508000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3302389"}},"subtitle":["Fast Implementations of the Brouwer-Zimmermann Algorithm for the Computation of the Minimum Distance of a Random Linear Code"],"short-title":[],"issued":{"date-parts":[[2019,6,5]]},"references-count":26,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,6,30]]}},"alternative-id":["10.1145\/3302389"],"URL":"https:\/\/doi.org\/10.1145\/3302389","relation":{},"ISSN":["0098-3500","1557-7295"],"issn-type":[{"value":"0098-3500","type":"print"},{"value":"1557-7295","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,6,5]]},"assertion":[{"value":"2017-05-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-01-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-06-05","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}