Systems and methods for decoding bose-chaudhuri-hocquenghem encoded codewords

A decoder for decoding a Bose-Chaudhuri-Hocquenghem (BCH) encoded codeword, the decoder comprising:

• a receiving module configured to receive a codeword over a data channel, the codeword having a first number of data bits, the first number is not greater than a preset value;
• a syndrome calculation module configured to determine a plurality of syndrome values for the codeword during a first time interval;
• an error locator polynomial module configured to generate an error locator polynomial based on the plurality of syndrome values, the error locator polynomial representing one or more errors in the codeword;
• an error location determination module configured to
• determine a set of initial elements during the first time interval, the set of initial elements being powers of a primitive element which are determined by a difference between the preset value and the first number;
• and
• evaluate, based on the set of initial elements, the error locator polynomial to identify one or more error locations corresponding to the one or more errors in the codeword;
• and
• an error correction module configured to correct the codeword based on the one or more error locations.