| In this thesis,we mainly discuss the existence of MDS almost self-dual codes over finite fields Fq.Let r be a power of odd prime.First we propose a method to construct MDS almost self-dual codes.Under the condition of q=r2 when using the second fundamental theorem of group homomorphism.Next,we briefly discuss the construction of MDS almost self-dual codes when q=r2s and q=rs.Finally,the trace function is applied to obtain:if there exists a q-ary MDS almost self-dual codes with length of n over Fq,then there exists a ql-ary MDS almost self-dual codes with length of nql-1 over Fql(l≥2).the norm function is applied to obtain:if there exists a q-ary MDS almost self-dual codes with length of n(1≤n≤q-1/2)over Fq(q≥3)and l is odd,then there exists a ql-ary MDS almost self-dual codes with length of nql-z/q-l over Fql.If l is even,then there exists a ql-ary MDS self-dual codes with length of over Fql.If there exists a q-ary MDS almost self-dual codes with length of n+1 over Fq,then there exists a ql-ary MDS almost self-dual codes with length of nql-z/q-l+1 over Fql(l≥2). |
