Algebraic Methods in Coding Theory

Abstract

The objective of the study is to easily and briefly describe algebraic error-correcting codes and their techniques. The necessary knowledge to read the paper is assumed mainly within elementary mathematics except for a part and we discuss them along with various examples. This is because the easiest method of understanding the algebraic coding theory is considered to be the calculation of their numerical examples. We start our description of the theory of linear feedback shift registers (LFSR) which are regarded to be a class of recurrence relations. Then, we treat Reed-Solomon codes, discrete Fourier transforms, and the basics of Gr¨obner bases in this paper.