Parameters and Decoding Performance of Subfield Subcodes of One-Point Elliptic Codes

It is known that subfield subcodes of Reed-Solomon (RS) codes include many good codes, such as BCH codes and classical Goppa codes. Extending the subfield subcode discovery from RS codes to the more general algebraic-geometric (AG) codes, this paper investigates the subfield subcodes of one-point elliptic codes, in order to provide an alternative to BCH codes. Lower bounds on the dimension and the minimum distance of these codes are characterized, which behave tight for the medium-to-high rate subfield subcodes of differential elliptic codes. The work will show that subfield subcodes of differential elliptic codes are superior to those of the evaluation ones. Many good codes and even the best known linear codes can be found in the family of these codes. With both the elliptic codes and the RS codes defined over the same field, near maximum likelihood (ML) decoding results show that some binary subfield subcodes of the elliptic codes outperform the similar rate BCH codes.