Number Theory and Algebra belong to the major areas of mathematics, and they can be applied to Coding Theory, a part of Information 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, and so on.
Furthermore, we focus on construction of "good" error-correcting codes, which is one of two major themes of Coding Theory for minimizing the loss of information transmitted through noisy channels. We study a variety of interesting code classes such as self-dual 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 (Self-dual codes, Cyclic codes, LCD codes, Convolutional codes, and etc) and cryptographic functions (bent functions, plateaued functions).