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Abstrak :
Reed Solomon (RS) codes is a mechanism to detect and correct burst of errors in data transmission and storage systems. It provides a solid introduction to foundation mathematical concept of Galois Field algebra and its application. With the development of digital hardware technology, the RS concepts were brought into reality, i.e. the implementation of RS codec chips. This paper presents the development steps of a generic RS encoder using VHDL. The encoder is able to handle generic width of data, variable length of information, number of error as well as variable form of primitive polynomial and generator polynomial used in the system. The design has been implemented for FPGA chip Xilinx XC3S200-5FT256 and has a better performance than commercially available equivalent encoder.

Abstrak :
ABSTRAK
Misalkan F_q^n merupakan himpunan semua n-pasangan terurut n-tuple elemen yang setiap koordinatnya merupakan elemen dari lapangan F_q, maka sebuah kode linier C merupakan subruang dari F_q^n dan biasa ditulis sebagai kode [n,k,d]. Misalkan A dan B merupakan kode linier atas F_ q^m dengan panjang n, maka A,B disebut t-error correcting pair t-ECP untuk C jika A B perp;C, k A >t, d B^ perp; >t, dan d A d C >n. Dalam penelitian ini ditunjukkan bahwa kode MDS non-GRS dan kode AMDS [n,1,n-1] memiliki 1-error-correcting pair. Selain itu, ditunjukkan bahwa kode AMDS [n,n-1,1] tidak memiliki error-correcting pair.

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ABSTRACT
Let F q n be the set of all n tuple element which each coordinate is an element of F q. A linear code C is a subspace of F q n and can be written as n,k,d code. Let A and B be linear codes over F q m with length n. Then A,B is called t error correcting pair t ECP for C if A B perp C, k A t, d B perp t, and d A d C n. This study shows that the non GRS MDS code and the AMDS n,1,n 1 code have 1 error correcting pair. This study also shows that the AMDS code n,n 1,1 has no error correcting pair.