Dr Sophie Huczynska
Reader
- Phone
- +44 (0)1334 46 3711
- sh70@st-andrews.ac.uk
- Office
- 312 MI
- Location
- Mathematical Institute
Biography
I joined the School in 2003, having obtained my PhD at the University of Glasgow and worked as a researcher at the University of Edinburgh. I held a Royal Society Dorothy Hodgkin Research Fellowship from 2004-2010, before becoming a Lecturer in 2010, Senior Lecturer in 2015 and Reader in 2023. I have worked part-time since 2008.
Research areas
My research interests are in the area of combinatorics and finite fields. I enjoy exploring a wide range of topics in these areas, including:
- structure theory of finite fields (including primitive and normal polynomials)
- existence and construction of difference structures such as partial difference sets and external difference families, using techniques such as cyclotomy and finite geometry
- application of combinatorial structures to coding theory and cryptography
- questions in additive combinatorics involving sumsets and additive tuples
- study of combinatorial objects such as graphs, digraphs and permutations viewed as relational structures.
More information about my research may be found on my personal website https://shuczynska.github.io/index.html
PhD supervision
- Struan McCartney
- Yayi Zhu
Selected publications
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Open access
Digraph-defined external difference families and new circular external difference families
Huczynska, S., Jefferson, C. & McCartney, S., 15 May 2026, In: Designs, Codes and Cryptography. 94, 5, 21 p., 110.Research output: Contribution to journal › Article › peer-review
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Open access
The intersection distribution: new results and perspectives
Huczynska, S., Klawuhn, L. & Paterson, M. B., 1 Sept 2026, In: Finite Fields and Their Applications. 114, 44 p., 102828.Research output: Contribution to journal › Article › peer-review
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Open access
Beyond uniform cyclotomy
Huczynska, S., Johnson, L. & Paterson, M. B., 1 Aug 2025, In: Finite Fields and Their Applications. 105, 23 p., 102604.Research output: Contribution to journal › Article › peer-review
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Open access
New results on non-disjoint and classical strong external difference families
Huczynska, S. & Hume, S., Jun 2025, In: Designs, Codes and Cryptography. 93, 6, p. 1985-2012 28 p.Research output: Contribution to journal › Article › peer-review
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Open access
Denniston partial difference sets exist in the odd prime case
Davis, J. A., Huczynska, S., Johnson, L. & Polhill, J., 1 Oct 2024, In: Finite Fields and Their Applications. 99, 13 p., 102499.Research output: Contribution to journal › Article › peer-review
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Open access
New constructions for disjoint partial difference families and external partial difference families
Huczynska, S. & Johnson, L., Apr 2024, In: Journal of Combinatorial Designs. 32, 4, p. 190-213 24 p.Research output: Contribution to journal › Article › peer-review
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Open access
Non-disjoint strong external difference families can have any number of sets
Huczynska, S. & Ng, S.-L., 30 Apr 2024, (E-pub ahead of print) In: Archiv der Mathematik. 11 p.Research output: Contribution to journal › Article › peer-review
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Open access
Internal and external partial difference families and cyclotomy
Huczynska, S. & Johnson, L., 1 Mar 2023, In: Discrete Mathematics. 346, 3, 24 p., 113295.Research output: Contribution to journal › Article › peer-review
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Open access
Strong external difference families in abelian and non-abelian groups
Huczynska, S., Jefferson, C. & Nepšinská, S., Mar 2021, In: Cryptography and Communications . 13, 2, p. 331–341 11 p.Research output: Contribution to journal › Article › peer-review
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Open access
Characterising bimodal collections of sets in finite groups
Huczynska, S. & Paterson, M., 9 Jul 2019, (E-pub ahead of print) In: Archiv der Mathematik. First Online, 10 p.Research output: Contribution to journal › Article › peer-review