Systematic modified Reed-Solomon codes

Systematic m-bit symbol codes are constructed by modifying (m+τ)-bit symbol Reed-Solomon (RS) codes. These new codes are called systematic modified Reed-Solomon (SMRS) codes and have code length that far exceeds 2^m, the length of m-bit RS codes. Although the systematic encoding of an SMRS code is slightly more complicated then that of the conventional RS codes, the decoding of the new code is exactly the same as that of the conventional RS codes. With one single 8-bit symbol SMRS code, it is now possible to protect entire 512-byte data sector of a data storage system, such as disk drive. It is also shown that 2^τ SMRS codes with distinct and fixed most significant τ-bits in all symbols of a code can be modified from a single RS code. Using these distinct SMRS codes for adjacent tracks in a disk drive, the probability that the correct track to be read at all time can be significantly enhanced