Polynomials over finite fields, semigroups and semigroup rings, and their applications

有限域上的多项式、半群和半群环及其应用

• 批准号: 312588-2007
• 负责人: Wang, Qiang(Steven)
• 金额: $ 0.73万
• 依托单位: Carleton University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2010
• 资助国家: 加拿大
• 起止时间: 2010-01-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=457499
• 关键词: Polynomials; over; finite; fields; semigroups

Polynomials over finite fields have attracted considerable interest due to their wide applications in coding theory, combinatorics and cryptography. One aspect of this research is the theoretical study of some arithmetic properties of polynomials and the theoretical study of their permutation behavior when applicable. Their connections with shift register sequences, combinatorial designs, and cryptanalysis are explored.

有限域上的多项式因其在编码理论、组合学和密码学中的广泛应用而引起人们的极大兴趣。这项研究的一个方面是多项式的一些算术性质的理论研究，以及多项式在适用时的置换行为的理论研究。探讨了它们与移位寄存器序列、组合设计和密码分析的关系。