A method for improving the code rate and error correction capability of a cyclic code

Currently, there has been an increasing demand for operational and trustworthy digital data transmission and storage systems. This demand has been augmented by the appearance of large-scale, high-speed data networks for the exchange, processing and storage of digital information in the different spheres. In this paper, we explore a way to achieve this goal. For given positive integers n,r, we establish that corresponding to a binary cyclic code C0[n,n-r], there is a binary cyclic code C[(n+1)3k-1,(n+1)3k-1-3kr], where k is a nonnegative integer, which plays a role in enhancing code rate and error correction capability. In the given scheme, the new code C is in fact responsible to carry data transmitted by C0. Consequently, a codeword of the code C0 can be encoded by the generator matrix of C and therefore this arrangement for transferring data offers a safe and swift mode. © 2013 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.

A decoding method of an n length binary BCH code through (n + 1)n length binary cyclic code

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A BCH code and a sequence of cyclic codes

This study establishes that for a given binary BCH code C0 n of length n generated by a polynomial g(x) ∈ F2[x] of degree r there exists a family of binary cyclic codes {Cm 2m−1(n+1)n}m≥1 such that for each m ≥ 1, the binary cyclic code Cm 2m−1(n+1)n has length 2m−1(n + 1)n and is generated by a generalized polynomial g(x 1 2m ) ∈ F2[x, 1 2m Z≥0] of degree 2mr. Furthermore, C0 n is embedded in Cm 2m−1(n+1)n and Cm 2m−1(n+1)n is embedded in Cm+1 2m(n+1)n for each m ≥ 1. By a newly proposed algorithm, codewords of the binary BCH code C0 n can be transmitted with high code rate and decoded by the decoder of any member of the family {Cm 2m−1(n+1)n}m≥1 of binary cyclic codes, having the same code rate.

CYCLIC CODES THROUGH B[X], B[X; 1/kp Z(0)] and B[X; 1/p(k) Z(0)]: A COMPARISON

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A decoding procedure which improves code rate and error corrections

Corresponding to $C_{0}[n,n-r]$, a binary cyclic code generated by a primitive irreducible polynomial $p(X)\in \mathbb{F}_{2}[X]$ of degree $r=2b$, where $b\in \mathbb{Z}^{+}$, we can constitute a binary cyclic code $C[(n+1)^{3^{k}}-1,(n+1)^{3^{k}}-1-3^{k}r]$, which is generated by primitive irreducible generalized polynomial $p(X^{\frac{1}{3^{k}}})\in \mathbb{F}_{2}[X;\frac{1}{3^{k}}\mathbb{Z}_{0}]$ with degree $3^{k}r$, where $k\in \mathbb{Z}^{+}$. This new code $C$ improves the code rate and has error corrections capability higher than $C_{0}$. The purpose of this study is to establish a decoding procedure for $C_{0}$ by using $C$ in such a way that one can obtain an improved code rate and error-correcting capabilities for $C_{0}$.

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.

Constructions of codes through the semigroup ring B[X; 1/2(2)Z(0)] and encoding

For any finite commutative ring B with an identity there is a strict inclusion B[X; Z(0)] subset of B[X; Z(0)] subset of B[X; 1/2(2)Z(0)] of commutative semigroup rings. This work is a continuation of Shah et al. (2011) [8], in which we extend the study of Andrade and Palazzo (2005) [7] for cyclic codes through the semigroup ring B[X; 1/2; Z(0)] In this study we developed a construction technique of cyclic codes through a semigroup ring B[X; 1/2(2)Z(0)] instead of a polynomial ring. However in the second phase we independently considered BCH, alternant, Goppa, Srivastava codes through a semigroup ring B[X; 1/2(2)Z(0)]. Hence we improved several results of Shah et al. (2011) [8] and Andrade and Palazzo (2005) [7] in a broader sense. Published by Elsevier Ltd

Encoding through generalized polynomial codes

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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.

Determination of Analgesics (Dipyrone and Acetaminophen) in Pharmaceutical Preparations by Cyclic Voltammetry at a Copper(II) Hexacyanoferrate(III) Modified Carbon Paste Electrode

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Selectivity of the cyclic carbonate formation by fixation of carbon dioxide into epoxides catalyzed by Lewis bases

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Changes in sodium, potassium-ATPase induced by repeated fencamfamine: the roles of cyclic AMP-dependent protein kinase and the nitric oxide-cyclic GMP pathway

Fencamfamine (FCF) is an indirect dopamine agent with effects similar to amphetamine and cocaine. In the present study, we investigate changes in Na,K-ATPase, cyclic AMP-dependent protein kinase (PKA) and nitric oxide synthase (NOS) activity and cyclic GMP levels in the nucleus accumbens (NAc) and striatum (ST) of animals acutely or repeatedly treated with FCF (3.5 mg/kg). Na,K-ATPase had a similar activity in control and repeatedly treated animals, but was reduced in the NAc of the acute group. This enzyme was reduced in the ST in acute and repeatedly treated animals, compared to the control group. Expression of the alpha(1,2,3)-Na,K-ATPase isoforms in the NAc and the ST was not altered in all groups studied. Acute FCF induced a significant increase in PKA activity in both the ST and the NAc. Repeatedly treated animals showed a higher increase in PKA activity in the NAc, but not in the ST, when compared to the acute group. There was also an increase in both NOS activity and cyclic GMP levels only in the NAc of FCF repeatedly treated animals compared to the acute and control groups. We suggest that chronic FCF treatment is linked to a modification in Na,K-ATPase activity through the PKA and NO-cyclic GMP pathway. (C) 2003 Elsevier Ltd. All rights reserved.

Repeated predictable or unpredictable stress: effects on cocaine-induced locomotion and cyclic AMP-dependent protein kinase activity

Stressful experiences appear to have a strong influence on susceptibility to drug taking behavior. Cross-sensitization between stress and drug-induced locomotor response has been found. Locomotor response to novelty or cocaine (10 mg/kg, i.p.), cyclic AMP-dependent protein kinase (PKA) activity in the nucleus accumbens and basal corticosterone levels were evaluated in male adult rats exposed to acute and chronic predictable or unpredictable stress. Rats exposed to a 14-day predictable stress showed increased locomotor response to novelty and to cocaine, whereas rats exposed to chronic unpredictable stress demonstrated increased cyclic AMP-dependent PKA activity in the nucleus accumbens. Both predictable and unpredictable stress increased basal corticosterone plasma levels. These experiments demonstrated that stress-induced early cocaine sensitization depends on the stress regime and is apparently dissociated from stress-induced changes in cyclic AMP-dependent PKA activity and corticosterone levels. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Identification of oligomers in polyethyleneterephthalate bottles for mineral water and fruit juice - Development and validation of a high-performance liquid chromatographic method for the determination of first series cyclic trimer

Cyclic oligomers were identified in PET bottles used for mineral water and fruit juice using MS and H-1 and C-13 NMR: a first series cyclic trimer, a first series cyclic tetramer, a first series cyclic dimmer and a second series cyclic trimer. An analytical method to determine first series cyclic trimer in these bottles was developed and validated, using HPLC. The first series cyclic trimer levels were 316-462 mg/100 g of PET bottle. (c) 2005 Elsevier B.V. All rights reserved.

Caffeine Determination at a Carbon Fiber Ultramicroelectrodes by Fast-Scan Cyclic Voltammetry

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