We give a classification of all double circulant doubly even self-dual [72, 36, 12] codes. We also demonstrate that every double circulant doubly even self-dual [72, 36, 12] code has no extremal doubly even self-dual [72, 36, 16] neighbor.

We investigate self-dual codes from a structural point of view. In particular, we study properties of critical indecomposable codes which appear in the spectrum of a self-dual code. As an application of the results we obtain, we revisit the study of self-dual codes of dimension at most 10.

When considering forward error correction (FEC) algorithms for telecommunication applications, the BCJR algorithm is the sub-optimal MAP (maximum a posteriori) soft decoding algorithm. For the case of high code rate, BCJR decoding based on the trellis in the dual domain is computationally much less complex than in the original domain. Previously, designs of dual domain primitive circuit element...

We describe the code PCx, a primal-dual interior-point code for linear programming. Information is given about problem formulation and the underlying algorithm, along with instructions for installing, invoking, and using the code. Computational results on standard test problems are tabulated. The current version number is 1.1.

Self-dual codes over Z2 ×Z4 are subgroups of Z2 ×Zβ4 that are equal to their orthogonal under an inner-product that relates to the binary Hamming scheme. Three types of self-dual codes are defined. For each type, the possible values α, β such that there exist a code C ⊆ Z 2 ×Z 4 are established. Moreover, the construction of a Z2Z4-linear code for each type and possible pair (α, β) is given. Fi...

We give a Decomposition Theorem for a family of Hopf algebras containing the well-know family of Taft Hopf algebras. Therefore, those indecomposable codes over this family of algebras (cf. [4]) is an indecomposable code over the studied case. We use properties of Hopf algebras to show that dual (in the module sense) of an ideal code is again an ideal code.

In this paper, we study self-dual codes over Z2× (Z2+uZ2), where u 2 = 0. Three types of self-dual codes are defined. For each type, the possible values α, β such that there exists a code C ⊆ Z2×(Z2+uZ2) β are established. We also present several approaches to construct self-dual codes over Z2 × (Z2 + uZ2). Moreover, the structure of two-weight self-dual codes is completely obtained for α · β 6...

Quadratic residue codes have been one of the most important classes of algebraic codes. They have been generalized into duadic codes and quadratic double circulant codes. In this paper we introduce a new subclass of double circulant codes, called duadic double circulant codes, which is a generalization of quadratic double circulant codes for prime lengths. This class generates optimal self-dual...

Dougherty, Gaborit, Harada, Munemasa, and Solé have previously given an upper bound on the minimum Lee weight of a Type IV self-dual -code, using a similar bound for the minimum distance of binary doubly even self-dual codes. We improve their bound, finding that the minimum Lee weight of a Type IV self-dual -code of length is at most 4 12 , except when = 4, and = 8 when the bound is 4, and = 16...

In this study, the results of parallelization of a 3-D dual code (Thin Layer, Parabolized Navier-Stokes solver) for solving supersonic turbulent flow around body and wing-body combinations are presented. As a serial code, TLNS solver is very time consuming and takes a large part of memory due to the iterative and lengthy computations. Also for complicated geometries, an exceeding number of grid...