Chien Search Using Multiple Basis Representation

A data storage system, comprising:

• one or more memories, wherein each memory of the one or more memories includes:
• a read/write unit;
• and
• a plurality of data storage cells;
• and
• a memory controller coupled to the one or more memories, wherein the memory controller is configured to:
• retrieve a code word stored in the one or more memories, wherein the code word is encoded with an Error Correction Code (ECC);
• generate one or more syndromes dependent upon the retrieved code word;
• determine an Error Locator Polynomial (ELP) dependent upon the generated syndromes, wherein the ELP is defined over a field, and wherein the ELP includes at least one root indicative of a location of an error within the code word;
• determine roots of the ELP;
• and
• decode the retrieved code word dependent upon the determined roots of the ELP.

A method of operating an Error Correction Code (ECC) decoder, comprising:

• receiving a code word, wherein the code word is encoded with an ECC;
• generating one or more syndromes dependent upon the received code word;
• determining an Error Locator Polynomial (ELP) dependent upon the generated syndromes, wherein the ELP is defined over a field, and wherein the ELP includes at least one root indicative of a location of an error within the code word;
• determining roots of the ELP;
• and
• decoding the received code word dependent upon the determined roots of the ELP.