几类MDS码和NMDS码的构造OA

MDS codes are optimal linear codes whose parameters achieve the Singleton bound.They are widely applied to distributed storage systems,random error channels and other related fields.NMDS codes have emerged as one of the hotspots in coding theory,as they can significantly reduce complexity of encoding and decoding while maintaining nearly the same error correction performance.The matrix is constructed by selecting the elements of the unit circle over finite field Fq2(where q is a power of 2).And a column vector is added to obtain a new matrix,which is used as a generator matrix to construct MDS codes and NMDS codes with length of(q+2).The weight enumerators of the constructed NMDS codes are determined.Then,subsets of Fqt(where t≥1 is an integer)of size l(4<l≤qt)are selected to construct MDS codes with length of l.The research shows that all MDS codes constructed are Griesmer codes,and all NMDS codes are near Griesmer codes.Meanwhile,the codebook indicates that all codes obtained are new.