New MDS or near MDS self-dual codes over finite fields
  The study of MDS self-dual codes has attracted lots of attention in recent years.   There are many papers on determining existence of $q-$ary MDS self-dual codes for various lengths.   There are not existence of $q-$ary MDS self-dual codes of some lengths, even these lengths $< q$.   We generalize MDS Euclidean self-dual codes to near MDS Euclidean self-dual codes and near MDS isodual codes.   And we obtain many new near MDS isodual codes from extended negacyclic duadic codes and we obtain many new MDS Euclidean self-dual codes from MDS Euclidean self-dual codes.   We generalize MDS Hermitian self-dual codes to near MDS Hermitian self-dual codes.   We obtain near MDS Hermitian self-dual codes from extended negacyclic duadic codes and from MDS Hermitian self-dual codes. 
Hongxi Tong, Xiaoqing Wang
cs.IT math.IT