Topic: Affine Codes and Multilinear Codes
Speaker: Juli Loisiana Butar-Butar
Time: 10a.m.–11a.m., Wednesday, 11 March 2026.
Room: 501 S1 building
In this weekly seminar, Our PhD student, Juli Loisiana Butar-Butar, presented the fundamental concepts of coding theory, focusing on linear codes, affine codes, and multilinear codes.
She began by motivating the study of coding theory through the concept of a communication channel, 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.
She then defined the notion of a code and codeword, followed by the Hamming distance, which measures the difference between two codewords. She explained how the minimum distance of a code determines its error-correcting capability.
The talk continued with an introduction to linear codes, 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.
In the next part, she introduced affine codes 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.
Finally, she introduced multilinear codes, extending linear codes to higher-dimensional settings. She explained their construction, support, and Hamming weight, and illustrated how they generalize classical coding theory concepts.