# Cyclic Codes of n < 26 and Comparison

The attached links are the group project paper and appendix in Cryptography course offered by Tommy Occhipinti in Carleton, Spring 2015: Crypt,Appendix.

The paper contains generating cyclic codes of length $n < 26$, comparing their parameters, and sorting out better ones.

# Character Table Project

The attached link is a group project in Representation Theory class offered by Eric Egge in Carleton, Spring 2015:Character Table.

The paper contains character tables of $A_4$, rotation of a cube, and $A_5$.

# Introduction to Mandelbrot Set

The attached link is a group project in Chaotic Dynamics Independent Studies in Spring 2015: Mandelbrot. The study and the project were under the supervision of Rafe Jones.

It introduces filled-in Julia set, Mandelbrot set and their properties. Plus, it covers graphical analysis of Mandelbrot set as well.

# Kummer’s Lemma and Cyclotomic Units

The attached link is a group project underwent in Analytic Number Theory class in Carleton College: Kummer. The course was offered by Rafe Jones in Winter 2014.

It proves Kummer’s Lemma, that is “Every unit of $\mathbb{Z}[\zeta_p]$ is of the form of $r\zeta_p^g$ where $r \in \mathbb{R}$ and $g \in \mathbb{Z}$.” Plus, it introduces Cyclotomic units and presents an example.

# Introduction to Hausdorff Measures and Fractals

The attached link is Senior Integrative Project in Carleton College that my group and I did over last term: COMPSFINAL. The project was underwent over Fall 2014 and Winter 2015 under supervision of Allison Tanguay.

The main purpose of the paper is to introduce the idea of Lebesgue measure and $\alpha$-dimensional Hausdorff measure, fractals and their behaviors, non-fractal sets and related conjecture.

Lee’s Challenge #1:

Consider an arbitrary non-negative real number, namely $\beta$. Can we always construct a set of which strict Hausdorff dimension is $\beta$?