Convenient Roots for a Reed Solomon Code
Original Publication Date: 1984-Jul-01
Included in the Prior Art Database: 2005-Feb-04
The Reed Solomon error correction code (RS code) has variations that lead to simpler parity generation and parity checking circuits. The text book example of an RS code with n parity symbols chooses some primitive field element a and uses a parity generator of the form: (Image Omitted) Working with symbols drawn from GF(2q), and with 5 parity symbols, this expands to: (Image Omitted) If polynomial (1) is changed so that i = -2, -1, 0, 1, 2, the expansion reduces to: (Image Omitted) This is more easily implemented, since there are fewer distinct coefficients.