Math at Ewha

2022. 3. 7. 오후 2:31

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Vision and Objectives

History of Department

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Calendar> Research Areas > Algebra and Representation Theory

Algebra and Representation Theory
Vision and Objectives
Prof. Yoonjin Lee

Prof. Se-jin Oh

History of Department

Research Areas
Algebra and Representation

Number Theory and Coding Theory Lab
Faculty Introduction

TheoryAnalysis and Partial
Differential Equations

Prof. Yoonjin Lee

Geometry and Topology

Office: Science Complex Building B room 313

Numerical Analysis

Tel: 02-3277-6653

Applied Analysis

Email: yoonjinl@ewha.ac.kr

Cryptography

Web: http://math.ewha.ac.kr/~yoonjinl

Undergraduate / Graduate

Research Area
- Algebraic Number Theory- Algebraic Coding Theory

Lab Introduction
Number Theory and Algebra belong to the major areas of mathematics, and they can be applied to Coding Theory, a part ofInformation Theory.
We broadly study the arithmetic of function fields and number fields: structure of class groups, non-vanishing of the L-functions
over function fields, surjectivity of Galois representations associated with Drinfeld modules, torsion groups of elliptic curves, andso on.
Furthermore, we focus on construction of "good" error-correcting codes, which is one of two major themes of Coding Theory forminimizing the loss of information transmitted through noisy channels. We study a variety of interesting code classes such as selfdual codes, cyclic codes, LCD codes, DNA codes, Quantum codes, Convolutional codes (Turbo codes) and so forth.
Graduate students in this lab currently study the arithmetic of function fields and number fields, a variety of algebraic codes (Selfdual codes, Cyclic codes, LCD codes, Convolutional codes, and etc) and cryptographic functions (bent functions, plateauedfunctions).

Major research projects and Research achievements

Number Theory• Arithmetic of number fields and function fields• Arithmetic of Drinfeld modules• Structure of ideal (or divisor) class groups of global function
fields and number fields• Non-vanishing of L-functions for various characters in function
fields• Modularity of various types of continued fractions• Torsion group structure of elliptic curves and hyperelliptic curves

Algebraic Coding Theory• Self-dual codes, Formally self-dual codes• Cyclic codes, Quasi-cyclic codes• Algebraic Geometric codes and Number field codes• Convolutional codes, LCD codes, DNA codes• Cryptographic functions: Bent functions andPlateaued functions• Strongly regular graphs, Few-weight codes

Selected research papers
Mathscinet

J. Lee, Y. Lee, Non-vanishing of L-functions for cyclotomic characters in function fields, To appear in Proc. Amer. Math. Soc.,
2021 (accepted for publication)
J. Yoo, Y. Lee, Infinite families of cyclic function fields with prescribed class group rank, Journal of Pure and Applied Algebra,
vol. 225 (2021), no. 9, 106658.
W.-H. Choi, H. J. Kim, Y. Lee, Construction of single-deletion-correcting DNA codes using CIS codes, Designs, Codes andCryptography, vol. 88 (2020), No. 12, 2581-2596.
J. Y. Hyun, J. Lee, Y. Lee, Infinite families of optimal linear codes constructed from simplicial complexes, IEEE Transactions
on Information Theory, Vol. 66, (2020), No. 11, 6762-6773.
H. J. Kim, W.-H. Choi, Construction of reversible self-dual codes, Finite Fields and their Applications, vol. 67 (2020), 101714.

Graduate StudentsNayoung Han Ph. D student
Research Area: algebraic coding theory, convolutional codes
Jihye Jeong Ph. D student
Research Area: algebraic coding theory, cryptographic functions
Siyun Lee Ph. D student
Research Area: number theory, arithmetic of number fields
Shin-Yoo Park Master's student
Research Area: algebraic coding theory
Woojung Choi Master's student
Research Area: algebraic coding theory

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