Introduction - If you have any usage issues, please Google them yourself
The Berlekamp multiplier [3] uses two basis representations, the polynomial basis
for the multiplier and the dual basis for the multiplicand and the product. Because it is
normal practice to input all data in the same basis, this means some basis transformation
circuits will be required. Fortunately for m = (3, 4, 5, 6, 7, 9, 10) the basis conversion
from the dual to the polynomial basis - and vice versa - is merely a reordering of the basis
coefficients [38]. For the important case m = 8 - for example the error-correcting systems
used in CDs, DAT and many other applications operate over GF(28) - this basis conversion
requires a reordering and two additions of the basis coefficients (Appendix C). In practice
therefore, two additional XOR gates are required. Even including the extra hardware for
basis conversions, the Berlekamp multiplier is known to have the lowest hardware
requirements of all available bit-serial multipliers [24].