Has anyone determined what 48-bit and 56-bit ECC polynomials are used by the National Semiconductor hard disk controllers? The DP8496/97 allows choice of hard-wired 16-bit CRC, or 32-bit, 48-bit, or 56-bit ECC. The 32-bit ECC is a common polynomial known as the Glover polynomial, and it's the same one used by WD and others. However, National was apparently extremely proud of the 48-bit and 56-bit polynomials they chose, and the data sheets say that they require a license agreement with National.
The more common DP8466 supports 32-bit 48-bit, but allows the user to configure the polynomial. The data sheet states that National's 48-bit polynomial is available under license. WD wasn't as proud of their 56-bit polynomial; it's given in the WD42C22 data sheet. It doesn't seem to match National Semicondutor's 56-bit polynomial.