In this report, the cyclic error correcting code: Reed Solomon code which is constructed by using Galois Field is presented to correct an error during transmission ofcode words in the noisy channel. Ifthe sender sends a code word c through noisy channel and when it reached at receiver ifit became w, then the receiver decode w to the most likely code word. This is decoded by using error locator polynomial.

Dissertation }' Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science in Mathematics