A new approach to the minimum distance of Goppa geometry codes
Wanbao Hu · 2007
A new approach to the bounds of the minimum distance of Goppa geometry codes(algebraic-geometric codes) is presented.We apply Maharaj′s idea,which use explicit bases to express approximately Riemann-Roch space,to the bounds of the minimum distance of Goppa′s Geometry codes.Then,by a class of examples from algebraic-geometric codes on Hermitian curves,we show that the Goppa′s standard lower bound of the codes can be improved significantly in some cases.We further give the upper bound of the minimum distance of the codes as well,and show that our lower bound is very close to our upper bound.