New directions in AMD codes over Galois fields and related structures

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As the world's data grows, secure and reliable data transmission presents an ever-increasing challenge. Addressing this requires cryptography, the study of secure communication, underpinned by mathematics. Algebraic manipulation detection (AMD) codes are designed against attacks where adversaries manipulate encoded messages, to trick recipients into wrongly decoding them. Designing the safest-possible AMD codes can be modelled mathematically by objects from combinatorics called external difference families and their generalizations. Up till now, the full potential of Galois field structure for AMD code construction has not been explored. This project will develop a deeper, more extensive structural framework for building optimal AMD codes in Galois fields, Galois domains and Galois rings.