New directions in AMD codes over Galois fields and related structures

随着全球数据量的增长，安全可靠的数据传输提出了越来越大的挑战。解决这个问题需要密码学，一种以数学为基础的安全通信研究。代数操纵检测（AMD）代码是针对攻击而设计的，攻击者操纵编码的消息，欺骗接收者错误地解码它们。设计最安全的AMD代码可以通过称为外部差分族的组合学对象及其泛化进行数学建模。到目前为止，伽罗瓦场结构在AMD代码构建中的全部潜力还没有被挖掘出来。该项目将开发一个更深入、更广泛的结构框架，用于在伽罗瓦域、伽罗瓦域和伽罗瓦环中构建最佳AMD代码。

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.