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Tag Archives: galois field
Evaluating Polynomials in an FPGA
Sometimes, a polynomial will need to be evaluated at a specific value in an algorithm. This might be used for curve fitting or interpolation. Another case is for Galois Fields and error correction, where high-degree polynomials are common. There is … Continue reading
Another Galois Field Multiply
After completing my Reed-Solomon decoder’s HDL, I decided to see how well it performed. The results weren’t as good as I expected. The limiting path was in the field math. A bit of simple pipelining allowed 250MHz operation on my … Continue reading
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Shifting an LFSR Multiple Times
One useful operation for a Galois Field is the multiplication by a constant value. This is very useful, as it allows very simple logic to be used to generate the product . This avoids the need to convert between polynomial … Continue reading
Basic Math In a Galois Field
A Galois Field presents unique challenges, as basic operations like addition and multiplication are different. This article addresses basic methods for addition, subtraction, multiplication, and division of field elements. FPGA considerations are included.
Intro to Galois LFSRs
There is another, natural way to write the code for an LFSR. This article describes the Galois implementation of an LFSR. This also shows how LFSRs are related to Galois fields. This implementation is claimed to be a bit faster … Continue reading