Polynomial expander for generating coefficients of a...

Details Polynomial expander for generating coefficients of a... Polynomial expander for generating coefficients of a...

2006-04-18

2006-04-18

Chase, Shelly (Department: 2133)

Error detection/correction and fault detection/recovery

Pulse or data error handling

Digital data error correction

Reexamination Certificate

active

07032162

ABSTRACT:
For generating coefficients of an expanded polynomial, n-roots, each respective coefficient is generated at a respective one of (n+1) coefficient storage registers at one of a first place at a right most place to a (n+1) place at a left most place. In addition, a temporary coefficient is stored as the respective coefficient that was at the first place in a prior clock cycle. Such coefficients are initialized, and then an ithorder multiplier output is generated by multiplying an ithorder root with the respective coefficient at the first place, and an ithorder adder output is generated by adding the temporary coefficient to the ithorder multiplier output. The respective coefficients at and to the right of an (i+1) place are shifted toward the right with the respective coefficient at the first place becoming the temporary coefficient. The ithorder adder output then becomes the respective coefficient at the (i+1) place. Such a process is performed an (i+1) times for the ithorder root with (i+1) clock cycles and for each of the n-roots, for i=1 to n, to generate the respective coefficients of the expanded polynomial.

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