In this paper, we propose two novel modulation concepts based on a simple maximum distance separable (MDS) code and show that these can achieve better error performance than index (IM) related schemes. the first concept, use amplitude phase levels to form MDS code, whereas, in second one, in-phase quadrature components of codeword elements are used construct code. We depict practical schemes fo...

Given any linear code C over a finite field GF(q) we show how C can be described in a transparent and geometrical way by using the associated Bruen–Silverman code. Then, specializing to the case of MDS codes we use our new approach to offer improvements to the main results currently available concerning MDS extensions of linear MDS codes. We also sharply limit the possibilities for constructing...

Motivated by the application of high-density data storage technologies, symbol-pair codes are proposed to protect against pair-errors in symbol-pair channels, whose outputs are overlapping pairs of symbols. The research of symbol-pair codes with large minimum pair-distance is interesting since such codes have the best possible error-correcting capability. A symbol-pair code attaining maximal mi...

Resumo Maximum Distance Separable (MDS) convolutional codes are characterized through the property that the free distance meets the generalized Singleton bound. The existence of free MDS convolutional codes over Zpr was recently discovered in [26] via the Hensel lift of a cyclic code. In this paper we further investigate this important class of convolutional codes over Zpr from a new perspectiv...

Knowledge mining from immense datasets requires fast, reliable and affordable tools for their visual and interactive exploration. Multidimensional scaling (MDS) is a good candidate for embedding of high-dimensional data into visually perceived 2-D and 3-D spaces. We focus here on the way to increase the computational performance of MDS in the context of interactive, hierarchical, visualization ...

In this paper we introduce a lowest density MDS array code which is applied to a Smart Meter network to introduce reliability. By treating the network as distributed storage with multiple sources, information can be exchanged between the nodes in the network allowing each node to store parity symbols relating to data from other nodes. A lowest density MDS array code is then applied to make the ...

AbstructA new family of MDS array codes is presenled. The code arrays contain p information columns and T indelpendent parity columns, each column consisting of p 1 bits, where p is a prime. We extend a previously known construction for 1 he case T = 2 to three and more parity columns. It is shown that when r = 3 such extension is possible for any prime p. For larger values of T , we give neces...

We study the problem of private function retrieval (PFR) in a distributed storage system. In PFR the user wishes to retrieve a linear combination of M messages stored in noncolluding (N,K) MDS coded databases while revealing no information about the coefficients of the intended linear combination to any of the individual databases. We present an achievable scheme for MDS coded PFR with a rate t...

The code-based McEliece and Niederreiter cryptosystems are promising candidates for post-quantum public-key encryption. Recently, q-ary concatenated codes over Gaussian integers were proposed the cryptosystem, together with one-Mannheim error channel, where values limited to Mannheim weight one. Due values, achieve a higher correction capability than maximum distance separable (MDS) bounded min...

Distributed storage codes have important applications in the design of modern storage systems. In a distributed storage system, every storage node has a probability to fail and once an individual storage node fails, it must be reconstructed using data stored in the surviving nodes. Computation load and network bandwidth are two important issues we need to concern when repairing a failed node. T...