Galois field multiply accumulator

A method of determining an error polynomial for decoding a Bose-Chaudhuri-Hocquenghem (BCH) code, comprising the steps of:

• computing a plurality of syndromes associated with a data signal having a BCH code embedded therein;
• feeding the syndromes to a plurality of Galois field multiply accumulators;
• calculating a plurality of minimum-degree polynomials associated with the BCH code, using the Galois field multiply accumulators;
• and
• generating an error polynomial based on the minimum-degree polynomials.

A Galois field multiply accumulator comprising:

• a Galois field multiplier having two operand inputs and an output;
• a Galois field adder having two operand inputs and an output, said output of said Galois field multiplier being connected to a first one of said inputs of said Galois field adder;
• a first multiplexer having at least two inputs, a select line, and an output, said output of said first multiplexer being coupled to a first one of said inputs of said Galois field multiplier, a first one of said inputs of said first multiplexer being connected to a first data line, and a second one of said inputs of said first multiplexer being connected to a constant zero value;
• a second multiplexer having at least two inputs, a select line, and an output, said output of said second multiplexer being coupled to a second one of said inputs of said Galois field multiplier, a first one of said inputs of said second multiplexer being connected to a second data line, and a second one of said inputs of said second multiplexer being connected to a constant one value;
• and
• a third multiplexer having at least two inputs, a select line, and an output, said output of said third multiplexer being coupled to a second one of said inputs of said Galois field adder, a first one of said inputs of said third multiplexer being connected to a third data line, and a second one of said inputs of said third multiplexer being connected to a constant zero value.

A decoder circuit comprising:

• a plurality of syndrome inputs;
• a plurality of Galois field multiply accumulators;
• and
• means for using said Galois field multiply accumulators to generate an error polynomial based on values provided at said syndrome inputs.