Methods, systems and computer-readable media for error correction

A system, comprising:

• at least one storage medium including a set of instructions for decoding a (n, k, d) cyclic code, which including a message section and a parity check section;
• at least one processor configured to communicate with the at least one storage medium, wherein when executing the set of instructions, the at least one processor is directed to:
• receive a word corresponding to the (n, k, d) cyclic code;
• construct a look-up table, wherein the look-up table includes k syndrome vectors and k error patterns;
• compute a syndrome vector of the received word by a hardware processor;
• determine a weight of the syndrome vector of the received word;
• determine whether the weight of the syndrome vector of the received word is more than the error-correcting capacity;
• decode the cyclic code by adding the received word and the syndrome vector when the weight of the syndrome vector of the received word is not more than the error-correcting capacity;
• and
• decode the received word by inverting bits in the message section in sequence and re-computing a syndrome vector of the inverted received word when the weight of the syndrome vector of the received word is more than the error-correcting capacity.