Linear codes over finite local rings in a chain

For a positive integer $t$, let \begin{equation*} \begin{array}{ccccccccc} (\mathcal{A}_{0},\mathcal{M}_{0}) & \subseteq & (\mathcal{A}_{1},\mathcal{M}_{1}) & \subseteq & & \subseteq & (\mathcal{A}_{t-1},\mathcal{M}_{t-1}) & \subseteq & (\mathcal{A},\mathcal{M}) \\ \cap & & \cap & & & & \cap & & \cap \\ (\mathcal{R}_{0},\mathcal{M}_{0}^{2}) & & (\mathcal{R}_{1},\mathcal{M}_{1}^{2}) & & & & (\mathcal{R}_{t-1},\mathcal{M}_{t-1}^{2}) & & (\mathcal{R},\mathcal{M}^{2}) \end{array} \end{equation*} be a chain of unitary local commutative rings $(\mathcal{A}_{i},\mathcal{M}_{i})$ with their corresponding Galois ring extensions $(\mathcal{R}_{i},\mathcal{M}_{i}^{2})$, for $i=0,1,\cdots,t$. In this paper, we have given a construction technique of the cyclic, BCH, alternant, Goppa and Srivastava codes over these rings. Though, initially in \cite{AP} it is for local ring $(\mathcal{A},\mathcal{M})$, in this paper, this new approach have given a choice in selection of most suitable code in error corrections and code rate perspectives.

Goppa codes over certain semigroups

A Goppa code is described in terms of a polynomial, known as Goppa polynomial, and in contrast to cyclic codes, where it is difficult to estimate the minimum Hamming distance d from the generator polynomial. Furthermore, a Goppa code has the property that d ≥ deg(h(X))+1, where h(X) is a Goppa polynomial. In this paper, we present a decoding principle for Goppa codes constructed by generalized polynomials, which is based on modified Berlekamp-Massey algorithm.

A Note on Linear Codes over Semigroup Rings

In this paper, we introduced new construction techniques of BCH, alternant, Goppa, Srivastava codes through the semigroup ring B[X; 1 3Z0] instead of the polynomial ring B[X; Z0], where B is a finite commutative ring with identity, and for these constructions we improve the several results of [1]. After this, we present a decoding principle for BCH, alternant and Goppa codes which is based on modified Berlekamp-Massey algorithm. This algorithm corrects all errors up to the Hamming weight t ≤ r/2, i.e., whose minimum Hamming distance is r + 1.

A new transmission model in cognitive radio based on cyclic generalized polynomial codes for bandwidth reduction

The frequency spectrums are inefficiently utilized and cognitive radio has been proposed for full utilization of these spectrums. The central idea of cognitive radio is to allow the secondary user to use the spectrum concurrently with the primary user with the compulsion of minimum interference. However, designing a model with minimum interference is a challenging task. In this paper, a transmission model based on cyclic generalized polynomial codes discussed in [2] and [15], is proposed for the improvement in utilization of spectrum. The proposed model assures a non interference data transmission of the primary and secondary users. Furthermore, analytical results are presented to show that the proposed model utilizes spectrum more efficiently as compared to traditional models.

Cyclic codes through B[X;(a/b)Z_0, with (a/b) in Q^{+} and b=a+1, and Encoding

Let B[X; S] be a monoid ring with any fixed finite unitary commutative ring B and is the monoid S such that b = a + 1, where a is any positive integer. In this paper we constructed cyclic codes, BCH codes, alternant codes, Goppa codes, Srivastava codes through monoid ring . For a = 1, almost all the results contained in [16] stands as a very particular case of this study.

Use of uniform designs in combination with neural networks for viral infection process development

This work aimed to compare the predictive capacity of empirical models, based on the uniform design utilization combined to artificial neural networks with respect to classical factorial designs in bioprocess, using as example the rabies virus replication in BHK-21 cells. The viral infection process parameters under study were temperature (34°C, 37°C), multiplicity of infection (0.04, 0.07, 0.1), times of infection, and harvest (24, 48, 72 hours) and the monitored output parameter was viral production. A multilevel factorial experimental design was performed for the study of this system. Fractions of this experimental approach (18, 24, 30, 36 and 42 runs), defined according uniform designs, were used as alternative for modelling through artificial neural network and thereafter an output variable optimization was carried out by means of genetic algorithm methodology. Model prediction capacities for all uniform design approaches under study were better than that found for classical factorial design approach. It was demonstrated that uniform design in combination with artificial neural network could be an efficient experimental approach for modelling complex bioprocess like viral production. For the present study case, 67% of experimental resources were saved when compared to a classical factorial design approach. In the near future, this strategy could replace the established factorial designs used in the bioprocess development activities performed within biopharmaceutical organizations because of the improvements gained in the economics of experimentation that do not sacrifice the quality of decisions.

A formalized optimum code search for q-ary trellis codes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)