Investigating Linear Codes via Commutative Algebra (18frg220)

Informally, a code is a way of representing information. Codes are studied by various scientific disciplines - such as information theory, electrical engineering, mathematics, and computer science - for the purpose of designing efficient and reliable data transmission methods. Some codes are constructed using methods from areas of mathematics such as linear algebra and algebraic geometry. In our work, we study properties of these codes by associating to them sets of points with multiplicity in multi-dimensional spaces. By investigating the structure and properties of these geometric objects with techniques pertaining to commutative algebra we are able to infer information about the code which reflects its error-correcting capabilities.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).