Explicit Construction of Global Function Fields with Many Rational Places. The use of error-correcting codes and cryptosystems is fundamental to the secure and reliable operation of many technological devices that we depend upon in our everyday lives. Essentially invisible, both coding theory and cryptography are essential for banking (ATM machines, e-banking), commerce (e-commerce), defense (cryptography) and entertainment (digital TV and radio, music CDs, DVDs). While certain families of "goo ....Explicit Construction of Global Function Fields with Many Rational Places. The use of error-correcting codes and cryptosystems is fundamental to the secure and reliable operation of many technological devices that we depend upon in our everyday lives. Essentially invisible, both coding theory and cryptography are essential for banking (ATM machines, e-banking), commerce (e-commerce), defense (cryptography) and entertainment (digital TV and radio, music CDs, DVDs). While certain families of "good" codes and cryptosystems can be constructed from specific function fields whose existence is guaranteed by abstract theory, often no actual construction for the function field is currently known. We aim to close this gap, making a greater range of "good" codes and cryptosystems available for practical applications.
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Chromatic polynomials, random graphs, and error-correcting codes: a unified approach to graph colouring problems. Through a unified approach involving cutting-edge results on chromatic polynomials, random graphs, matroids, and error-correcting codes, this project will establish the foundations for a rigorous mathematical framework for attempting to provide a short, transparent and illuminating solution to the Four Colour Problem. The project will support developments in computer science and sta ....Chromatic polynomials, random graphs, and error-correcting codes: a unified approach to graph colouring problems. Through a unified approach involving cutting-edge results on chromatic polynomials, random graphs, matroids, and error-correcting codes, this project will establish the foundations for a rigorous mathematical framework for attempting to provide a short, transparent and illuminating solution to the Four Colour Problem. The project will support developments in computer science and statistical mechanics and is likely to have flow-on effects in real-world disciplines such as network communication. This project will also strengthen Australia's international presence in discrete mathematics and will further strengthen ties between Australian and international mathematicians.Read moreRead less
Special Research Initiatives - Grant ID: SR0354793
Funder
Australian Research Council
Funding Amount
$10,000.00
Summary
A Neural Network: Understanding Brain Function. This proposal focuses on the mechanisms that regulate brain function, particularly those underpinning the changes in circuitry (plasticity) caused by altered inputs. As such, its core goal is to create an interface between researchers in the neurosciences, computational modelling, robotics and cognitive sciences in order to facilitate optimum collaborative interactions, identify key research questions and promote training opportunities across a mul ....A Neural Network: Understanding Brain Function. This proposal focuses on the mechanisms that regulate brain function, particularly those underpinning the changes in circuitry (plasticity) caused by altered inputs. As such, its core goal is to create an interface between researchers in the neurosciences, computational modelling, robotics and cognitive sciences in order to facilitate optimum collaborative interactions, identify key research questions and promote training opportunities across a multidisciplinary spectrum. This will drive an integrated and accelerated program of discovery and technological development, enhancing Australia's leadership in this crucial field and helping to highlight new biotechnology opportunities and capture social and economic benefits for the nation. Read moreRead less