Speaker: <\/strong>Juli Loisiana Butar-Butar
Time:<\/strong> 10a.m.\u201311a.m., Wednesday, 11 March 2026.
\nRoom:<\/strong> 501 S1 building<\/p>\n
In this weekly seminar, Our PhD student, Juli Loisiana Butar-Butar,\u00a0presented the fundamental concepts of coding theory<\/strong>, focusing on linear codes, affine codes, and multilinear codes.<\/p>\n She began by motivating the study of coding theory through the concept of a communication channel<\/strong>, explaining how messages transmitted over noisy channels may encounter errors. To address this, she introduced the idea of encoding with redundancy, which allows error detection and correction.<\/p>\n She then defined the notion of a code<\/strong> and codeword<\/strong>, followed by the Hamming distance<\/strong>, which measures the difference between two codewords. She explained how the minimum distance of a code determines its error-correcting capability.<\/p>\n The talk continued with an introduction to linear codes<\/strong>, described as vector subspaces over finite fields. She explained the role of a generator matrix in constructing codewords and introduced the concept of Hamming weight, showing its connection to the minimum distance. She also discussed the dual code and introduced syndrome decoding as a method for detecting and correcting errors.<\/p>\n In the next part, she introduced affine codes<\/strong> as cosets of linear codes and explained how their structure differs from linear codes. She showed how properties of linear codes extend naturally to affine codes.<\/p>\n Finally, she introduced multilinear codes<\/strong>, extending linear codes to higher-dimensional settings. She explained their construction, support, and Hamming weight, and illustrated how they generalize classical coding theory concepts.<\/p>\n \n <\/p>","protected":false},"excerpt":{"rendered":" Topic: Affine Codes and Multilinear CodesSpeaker: Juli Loisiana Butar-ButarTime: 10a.m.\u201311a.m., […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-572","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/posts\/572","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/comments?post=572"}],"version-history":[{"count":3,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/posts\/572\/revisions"}],"predecessor-version":[{"id":579,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/posts\/572\/revisions\/579"}],"wp:attachment":[{"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/media?parent=572"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/categories?post=572"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/tags?post=572"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/algebra.math-ugm.id\/wp-content\/uploads\/2026\/03\/WhatsApp-Image-2026-03-11-at-10.38.59-1024x576.jpeg\")
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