1-2hit |
Tomoharu SHIBUYA Ryutaroh MATSUMOTO Kohichi SAKANIWA
In this paper, we present a lower bound for the dimension of subfield subcodes of residue Goppa codes on the curve Cab, which exceeds the lower bound given by Stichtenoth when the number of check symbols is not small. We also give an illustrative example which shows that the proposed bound for the dimension of certain residue Goppa code exceeds the true dimension of a BCH code with the same code length and designed distance.
Tomoharu SHIBUYA Ryutaroh MATSUMOTO Kohichi SAKANIWA
In this paper, we give a new lower bound for the dimension of subfield subcodes. This bound improves the lower bound given by Stichtenoth. A BCH code and a subfield subcode of algebraic geometric code on a hyper elliptic curve are discussed as special cases.