Network coding is an elegant and novel technique introduced at the turn of the millennium to improve network throughput and performance . It is expected to be a critical technology for networks of the future . The fundamental result of linear network coding asserts the existence of optimal linear network codes over multicast networks when the symbol alphabet is sufficiently large . In a Linear network code , intermediate nodes perform linear operations , so through each edge flows a linear combination of the symbols generated by the sources . The coefficients of this linear combination form a vector called the global encoding kernels (GEKs) and the coefficients of the linear operation are called the local encoding kernels (LEKs) . A linear network code can be described by either GEKs or LEKs . In the literature , the optimal properties of a linear network code such as multicast and MDS properties , are described by GEKs . In this thesis , some formulas are proposed to describe these properties by LEKs rather than GEKs . Designing optimal network codes for cyclic networks has attracted a lot of attentions because of their applications in practice . Due to the lack of upstream-to-downstream ordering over some cyclic networks , linear network code construction for cyclic networks is more complex than acyclic networks . In this thesis , a unified framework is proposed for designing optimal linear network codes over error-free , erroneous , constant-rate , variable-rate , cyclic and acyclic networks . The algorithms in these framework are based on LEKs , whereas all existing algorithms in the literature are based on GEKs . This thesis is organized in fourth part . In the first part , a method is proposed for constructing generic linear network codes using transversal matroids . A generic linear network code is the strongest optimal linear network code in terms of the linear independency of the coding vectors . It can be designed by constructing a representation matrix for a transversal matroid . In this part , first details on the method of constructing a GLN code using transversal matroids is presented , and then propose an algorithm to construct a representation matrix for a given transversal matroid which is faster than the only known algorithm in the literature . In the second part , by iiring the methods applied in the first part , first a formula is presented to describe the multicast property using LEKs rather than GEKs , and then this formula is used to develop an algorithm for designing multicast linear network codes over cyclic networks . In the third part , by generalizing the methods applied in the second part , first a formula is presented to describe the MDS property using LEKs rather than GEKs and then this formula is used to develop an algorithm for designing multicast MDS linear network codes over erroneous cyclic networks . In order to use network coding theory for variable rate erroneous acyclic networks , it was suggested the concept of a family of multicast MDS linear network codes that is a set of multicast MDS codes with the same LEKs in non-source nodes . But the codes in this family may have not the same GEKs . In the fourth part , it is shown that there is a family of multicast MDS linear network codes for cyclic and acyclic erroneous variable rate networks that not only have the same LEKs but also have almost the same GEKs . For this , it is introduced variable rate multicast MDS linear network code . This code is designed such that if some dimensions of this code is removed , then it holds its multicast MDS property . In other word , a variable rate multicast MDS linear network code play role of a family of multicast MDS linear network codes that have the same LEKs , and GEKs of a code in this family can be obtained by removing some dimension of GEKs of another code in this family . In this part , an algorithm is proposed for designing variable rate MDS linear network codes .