Will give a Discrete Mathematics Seminar entitled:
Building Codes from Disjunct Matrices
Abstract: Parity-check codes are a class of linear codes defined by their parity-check matrices. Disjunct matrices are used extensively in combinatorial group testing but were not previously well-studied as parity-check matrices for binary linear codes. I will give results on code parameters including rate, distance, and girth for both codes from general disjunct matrices and codes obtained via the Kautz-Singleton construction for superimposed codes. The Kautz-Singleton construction uses Reed-Solomon codes, a class of algebraic geometry codes defined using sets of polynomials. The talk will be accessible to those without previous knowledge of parity-check codes and combinatorial group testing.
Date: 09-22-2025
Time: 3:00 pm
Location: 129 Hayes-Healy Center