Construction Of Self-dual Codes Over Finite Commutative Frobenius Local Rings

There are several methods for constructing self-dual codes over finite rings. Among them, the building-up method is a powerful method using short self-dual codes to construct longer ones. Building-up method has been applied to self-dual codes over finite fields and some finite rings. Recently, Sunghyu Han proposed a method for constructing self-dual codes over the residue module integer 2m ring Z2m. This approach is a building-up approach with matrix form. In this paper, we use the matrix form to develop a building-up approach for constructing self-dual and self-orthogonal codes over finite commutative Frobenius local rings.In this paper, we firstly state the first building-up method for constructing self-dual codes over finite commutative Frobenius local rings with matrix form. Then, we prove that a self-dual codes with free rank k≥2, minimum Hamming distance d≥2, can be built from a shorter self-dual codes. Secondly, changing some conditions of the first construction method, we can get the second construction method, and we show that the two methods are one to one correspondence.Self-dual codes are a special kind of self-orthogonal codes. At last, we gener-alize the building-up methods which we proposed for constructing self-dual codes to construct self-orthogonal codes. We get two different methods to construct self-orthogonal codes and the two methods are one to one correspondence although their construction conditions are different.