BCH 코드왿� Reed Solomon 코드

Ⅰ BCH 소개
■ BCH (Bose –- Chaudhuri - Hocquenghem) Codes form a large class of multiple random error-correcting codes. They were first discovered by A. Hocquenghem in 1959 and independently by R. C. Bose and D. K. Ray-Chaudhuri in 1960.
■ BCH codes are cyclic codes. Only the codes, not the decoding algorithms, were discovered by these early writers.
■ The original applications of BCH codes were restricted to binary codes of length 2m −. 1 for some integer m. These were extended later by Gorenstein and Zieler (1961) to the nonbinary codes with symbols from Galois field GF(q).
■ The first decoding algorithm for binary BCH codes was devised by Peterson in 1960. Since then, eterson’`s algorithm has been refined by Berlekamp, Massey, Chien, Forney, and many others.

Ⅱ BCH 부호의 정의 및 부호화
■ BCH 부호는 Cyclic Code왿� 마찬가지로 Generator Polynomial을 이용하거나 생성 행렬을 이용하여 부호화 한다.
■ 2진 BCH 부호의 생성 다항식은 g(x) a, a², a³, a⁴..... a^2m을 근으로 가지는 최소다항식의 곱으로 표시된다.
■ 생성 다항식을 구하는 순서는 다음과 같다.
- 부호어의 길 n을 먼저 결정을 한다.