On Justesen’s algebraic geometry codes

Abstract

An isomorphism preserving Hamming distance between two algebraic geometry (AG) codes is presented to obtain the main parameters of Justesen’s algebraic geometry (JAG) codes. To deduce a simple approach to the decoding algorithm, a code word in a “small” JAG code is used to correspond to error-locator polynomial. By this means, a simple decoding procedure and its ability of error correcting are explored obviously. The lower and upper bounds of the dimension of AG codes are also obtained.