An effective error correction using a combination of algebraic geometric codes and Parity codes for HDD

This paper describes the performance of an efficient error-correcting system for hard disk drives. The performance of the codes on algebraic curves, such as Hermitian codes over GF(2⁸), elliptic codes over GF(2⁹), and Fermat codes over GF(2¹⁰) is compared with that of conventional Reed-Solomon (RS) codes. In particular, an adoption of Hermitian codes can reduce the redundant part by approximately 800 bits more than the RS codes when an error-correcting capability of 240 bytes is adopted for a long sector size. Moreover, we propose an error-correcting system based on a combination of algebraic geometric codes and parity codes. This combination system can cover a bit-error rate of approximately 10^-2 under a condition of EEPR4 channel and additive Gaussian noise.