In the area of network coding, linear code can achieve the maximum capacity of multicast networks by a large enough alphabet. And it is insufficient for non-multicast networks. Meanwhile nonlinear code is of interest for its possibility to achieve the network coding capacity by small alphabet, or its possibility to deal with other networks. In this paper, a novel polynomial code is proposed. We...

A (left) group code of length n is a linear code which is the image of a (left) ideal of a group algebra via an isomorphism FG→ F which maps G to the standard basis of F. Many classical linear codes have been shown to be group codes. In this paper we obtain a criterion to decide when a linear code is a group code in terms of its intrinsical properties in the ambient space F, which does not assu...

in this work, the mechanism for fracture of brittle substances such as rocks under a uniform normal tension is considered. the oriented straight micro-cracks are mostly created in all the polycrystalline materials resulting from the stress concentrations. the present work focuses on the interactions of the pre-existing micro-cracks, which can grow and propagate within a rock-like specimen. the ...

accurate prediction of pollution control and environmental protection need a good understanding of pollutant dynamics. numerical model techniques are important apparatus in this research area. so a 2500 line fortran 95 version code was conducted in which using approximate riemann solver, couples the shallow water and pollution transport agents in two dimensions by the aid of unstructured meshes...

Certain nonlinear binary codes contain more codewords than any comparable linear code presently known. These include the Kerdock and Preparata codes, which exist for all lengths 4m ≥ 16. At length 16 they coincide to give the Nordstrom-Robinson code. This paper constructs a nonlinear (64, 237, 12) code as the binary image, under the Gray map, of an extended cyclic code defined over the integers...

It is known that some good linear codes over a finite ring (R-linear codes) arise from interesting point constellations in certain projective geometries. For example, the expurgated Nordstrom-Robinson code, a nonlinear binary [14, 6, 6]-code which has higher minimum distance than any linear binary [14, 6]-code, can be constructed from a maximal 2-arc in the projective Hjelmslev plane over Z4. W...

In this correspondence, we investigate two important structural properties of block 2tary PSK modulation codes, namely: linear structure and phase symmetry. For an AWGN channel, the error performance of a modulation code depends on its squared Euclidean distance distribution. Linear structure of a code makes the error performance analysis much easier. Phase symmetry of a code is important in re...

In article present measure code distance algorithm of binary and ternary linear block code using block Korkin-Zolotarev (BKZ). Proved the upper bound on scaling constant for measure code distance of non-systematic linear block code using BKZ-method for different value of the block size. Introduced method show linear decrease of runtime from number of threads and work especially good under not d...

A Z2Z4-linear Hadamard code of length α + 2β = 2 t is a binary Hadamard code which is the Gray map image of a Z2Z4-additive code with α binary coordinates and β quaternary coordinates. It is known that there are exactly b t−1 2 c and b t 2c nonequivalent Z2Z4-linear Hadamard codes of length 2t, with α = 0 and α 6= 0, respectively, for all t ≥ 3. In this paper, it is shown that each Z2Z4-linear ...

This paper is concerned with the trellis structure of linear block codes. The paper consists of four parts. In the first part, we investigate the state and branch complexities of a trellis diagram for a linear block code. A trellis diagram with the minimum number of states is said to be minimal. First, we express the branch complexity of a minimal trellis diagram for a linear block code in term...