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In the theory of difference sets, there are two main directions. One is to find new construction and the other is to find conditions for nonexistence results. With my colleague Ma Siu Lun, we were the pioneer in using finite Galois rings to contruct Partial differnce sets in a series of our papers in Bulltein of London Mathematical Society. After that, quite a number of new constructions employ the same type of Galois rings are found.
We have also proved a number of nonexistence results on difference sets. One major breakthrough in this direction is our paper in Transaction of American Mathematical Society. In that paper, we have solved a special case of a long standing Landers' conjecture.
My long term goal is to develop more techniques to solve problems in difference sets and related topics.
There are also quite a number of combinatoric objects relating to difference sets. Recently, I have been working with my collaborators on circulant matrices. I started working with Bernhard Schmidt from NTU on circulant matrices since last year. We have written and submitted one paper and we are in the process of finalizing the second paper. In the upcoming paper, we have developed new techniques to settle some open known cases on circulant matrices. The third paper we have in mind is an improvement on paper we have submitted. With our colleagues, we are also working on another paper dealing with circulant matrices of small order.
Besides working on circulant matrices, I managed to write a paper with my friend from San Jose State University. While I visited him during my sabbatical, we worked out a key step he and his student needed. As a result, a paper was written and has been accepted by Bulletin of Australian Mathematical Society.
In the theory of difference sets, there are two main directions. One is to find new construction and the other is to find conditions for nonexistence results. With my colleague Ma Siu Lun, we were the pioneer in using finite Galois rings to contruct Partial differnce sets in a series of our papers in Bulltein of London Mathematical Society. After that, quite a number of new constructions employ the same type of Galois rings are found.
We have also proved a number of nonexistence results on difference sets. One major breakthrough in this direction is our paper in Transaction of American Mathematical Society. In that paper, we have solved a special case of a long standing Landers' conjecture.
My long term goal is to develop more techniques to solve problems in difference sets and related topics.
There are also quite a number of combinatoric objects relating to difference sets. Recently, I have been working with my collaborators on circulant matrices. I started working with Bernhard Schmidt from NTU on circulant matrices since last year. We have written and submitted one paper and we are in the process of finalizing the second paper. In the upcoming paper, we have developed new techniques to settle some open known cases on circulant matrices. The third paper we have in mind is an improvement on paper we have submitted. With our colleagues, we are also working on another paper dealing with circulant matrices of small order.
Besides working on circulant matrices, I managed to write a paper with my friend from San Jose State University. While I visited him during my sabbatical, we worked out a key step he and his student needed. As a result, a paper was written and has been accepted by Bulletin of Australian Mathematical Society.
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Designs, Codes and Cryptography (2024)
Designs, Codes and Cryptographypp.1-24, (2024)
DESIGNS CODES AND CRYPTOGRAPHY (2024)
JOURNAL OF COMBINATORIAL THEORY SERIES A (2023)
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J. Comb. Theory, Ser. A (2023)
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Journal of Combinatorial Theory, Series A (2020)
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