Reversible Codes Research Articles

DNA Code from Cyclic and Skew Cyclic Codes over F4[v]/⟨v3⟩

The main motivation of this work is to study and obtain some reversible and DNA codes of length n with better parameters. Here, we first investigate the structure of cyclic and skew cyclic codes over the chain ring R:=F4[v]/⟨v3⟩. We show an association between the codons and the elements of R using a Gray map. Under this Gray map, we study reversible and DNA codes of length n. Finally, several new DNA codes are obtained that have improved parameters than previously known codes. We also determine the Hamming and the Edit distances of these codes.

Reversible codes and applications to DNA codes over $ F_{4^{2t}}[u]/(u^2-1) $

<abstract><p>Let $ n \geq 1 $ be a fixed integer. Within this study, we present a novel approach for discovering reversible codes over rings, leveraging the concept of $ r $-glifted polynomials. This technique allows us to achieve optimal reversible codes. As we extend our methodology to the domain of DNA codes, we establish a correspondence between $ 4t $-bases of DNA and elements within the ring $ R_{2t} = F_{4^{2t}}[u]/(u^{2}-1) $. By employing a variant of $ r $-glifted polynomials, we successfully address the challenges of reversibility and complementarity in DNA codes over this specific ring. Moreover, we are able to generate reversible and reversible-complement DNA codes that transcend the limitations of being linear cyclic codes generated by a factor of $ x^n-1 $.</p></abstract>

Acceptability and feasibility of a planned preconception weight loss intervention in women with long-acting reversible contraception: the Plan-it mixed-methods study

Women with overweight (a body mass index of ≥ 25 kg/m2) or obesity (a body mass index of ≥ 30 kg/m2) are at greater risk of experiencing complications during pregnancy and labour than women with a healthy weight. Women who remove their long-acting reversible contraception (i.e. coils or implants) are one of the few groups of people who contact services as part of their preparation for conception, creating an opportunity to offer a weight loss intervention. The objectives were to understand if routine NHS data captured the pathway from long-acting reversible contraception removal to pregnancy and included body mass index; to identify the suitable components of a preconception weight loss intervention; and to engage with key stakeholders to determine the acceptability and feasibility of asking women with overweight/obesity to delay the removal of their long-acting reversible contraception in order to take part in a preconception weight loss intervention. This was a preparatory mixed-methods study, assessing the acceptability and feasibility of a potential intervention, using routine NHS data and purposefully collected qualitative data. The NHS routine data included all women with a long-acting reversible contraception code. There were three groups of participants in the surveys and interviews: health-care practitioners who remove long-acting reversible contraception; weight management consultants; and women of reproductive age with experience of overweight/obesity and of using long-acting reversible contraception. UK-based health-care practitioners recruited at professional meetings; and weight management consultants and contraceptive users recruited via social media. Anonymised routine data from UK sexual health clinics and the Clinical Practice Research Datalink, including the Pregnancy Register; and online surveys and qualitative interviews with stakeholders. The records of 2,632,871 women aged 16-48 years showed that 318,040 had at least one long-acting reversible contraception event, with 62% of records including a body mass index. Given the identified limitations of the routine NHS data sets, it would not be feasible to reliably identify women with overweight/obesity who request a long-acting reversible contraception removal with an intention to become pregnant. Online surveys were completed by 100 health-care practitioners, four weight management consultants and 243 contraceptive users. Ten health-care practitioners and 20 long-acting reversible contraception users completed qualitative interviews. A realist-informed approach generated a hypothesised programme theory. The combination of weight discussions and the delay of long-acting reversible contraception removal was unacceptable as an intervention to contraceptive users for ethical and practical reasons. However, a preconception health intervention incorporating weight loss could be acceptable, and one potential programme is outlined. There was very limited engagement with weight management consultants, and the sample of participating stakeholders may not be representative. An intervention that asks women to delay long-acting reversible contraception removal to participate in a preconception weight loss intervention would be neither feasible nor acceptable. A preconception health programme, including weight management, would be welcomed but requires risk communication training of health-care practitioners. Work to improve routine data sets, increase awareness of the importance of preconception health and overcome health-care practitioner barriers to discussing weight as part of preconception care is a priority. This trial is registered as ISRCTN14733020. This project was funded by the National Institute for Health and Care Research (NIHR) Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 27, No. 1.

Reversible Cyclic Codes over F2+uF2+u2F2

In this article, we investigate the formation of reversible cyclic codes (i.e., its codewords forms a symmetry) over the ring S=F2+uF2+u2F2, where u3=0. We find a unique set of generators for cyclic codes over S and classify reversible cyclic codes to their generators. The dual reversible cyclic codes are studied as well. Moreover, we provide some examples of reversible cyclic codes.

Neural Estimation of the Rate-Distortion Function With Applications to Operational Source Coding

A fundamental question in designing lossy data compression schemes is how well one can do in comparison with the rate-distortion function, which describes the known theoretical limits of lossy compression. Motivated by the empirical success of deep neural network (DNN) compressors on large, realworld data, we investigate methods to estimate the rate-distortion function on such data, which would allow comparison of DNN compressors with optimality. While one could use the empirical distribution of the data and apply the Blahut-Arimoto algorithm, this approach presents several computational challenges and inaccuracies when the datasets are large and high-dimensional, such as the case of modern image datasets. Instead, we reformulate the rate-distortion objective, and solve the resulting functional optimization problem using neural networks.We apply the resulting rate-distortion estimator, called NERD, on popular image datasets, and provide evidence that NERD can accurately estimate the rate-distortion function. Using our estimate, we show that the rate-distortion achievable by DNN compressors are within several bits of the rate-distortion function for realworld datasets. Additionally, NERD provides access to the ratedistortion achieving channel, as well as samples from its output marginal. Therefore, using recent results in reverse channel coding, we describe how NERD can be used to construct an operational one-shot lossy compression scheme with guarantees on the achievable rate and distortion. Experimental results demonstrate competitive performance with DNN compressors.

Reversible complement cyclic codes over ℤ4 + uℤ4 + vℤ4 for DNA computing

In this paper, we develop a theory for constructing cyclic codes of odd length over the ring [Formula: see text], where [Formula: see text], which plays an important role in DNA computing. A direct link between the elements of [Formula: see text] and the [Formula: see text] codons used in the amino acids of the living organisms is established. Then, we investigate reversible cyclic codes and reversible complement cyclic codes of odd length over [Formula: see text]. Moreover, we give some properties of binary images of the codons under the Gray map. Finally, two examples of cyclic codes over [Formula: see text] with their minimum Hamming distance will be studied as well.

Error Control Coding Algorithms in High Reliability Telemetry Systems

In the oil and gas industry, in the process of drilling support (geosteering) and well telemetry, there is a problem of transmitting reliable information via wireless communication channels. The quality of such communication, as a rule, suffers due to the presence of errors caused by interference. As the depth of the well increases, the problem becomes more extensive. In order to solve the problem, it is proposed to choose noise-resistant coding in the system of residual classes. This system parallelizes the execution of arithmetic operations, has corrective abilities and organically adapts to the neural network basis of intelligent field management. At the same time, there are constraining factors for the mass application of the RNS; for example, difficulties in implementing non-modular procedures, forward and reverse coding, and some difficulties in identifying and correcting errors. That is why the task of improving the RNS seems relevant not only for oil and gas complexes, but also for any digital signal processing applications focused on intelligent neural network management on the basis of non-positional computing. The material of the article is limited to the study of the noise immunity of linear codes of the deduction system and the development of algorithms for detecting and correcting errors.

Group LCD and group reversible LCD codes

In this paper, we give a new method for constructing LCD codes. We employ group rings and a well known map that sends group ring elements to a subring of the n×n matrices to obtain LCD codes. Our construction method guarantees that our LCD codes are also group codes, namely, the codes are ideals in a group ring. We show that with a certain condition on the group ring element v, one can construct non-trivial group LCD codes. Moreover, we also show that by adding more constraints on the group ring element v, one can construct group LCD codes that are reversible. We present many examples of binary group LCD codes of which some are optimal and group reversible LCD codes with different parameters.

Automation of reversible steganographic coding with nonlinear discrete optimisation

Authentication mechanisms are at the forefront of defending the world from various types of cybercrime. Steganography can serve as an authentication solution through the use of a digital signature embedded in a carrier object to ensure the integrity of the object and simultaneously lighten the burden of metadata management. Nevertheless, despite being generally imperceptible to human sensory systems, any degree of steganographic distortion might be inadmissible in fidelity-sensitive situations such as forensic science, legal proceedings, medical diagnosis and military reconnaissance. This has led to the development of reversible steganography. A fundamental element of reversible steganography is predictive analytics, for which powerful neural network models have been effectively deployed. Another core element is reversible steganographic coding. Contemporary coding is based primarily on heuristics, which offers a shortcut towards sufficient, but not necessarily optimal, capacity–distortion performance. While attempts have been made to realise automatic coding with neural networks, perfect reversibility is unattainable via such learning machinery. Instead of relying on heuristics and machine learning, we aim to derive optimal coding by means of mathematical optimisation. In this study, we formulate reversible steganographic coding as a nonlinear discrete optimisation problem with a logarithmic capacity constraint and a quadratic distortion objective. Linearisation techniques are developed to enable iterative mixed-integer linear programming. Experimental results validate the near-optimality of the proposed optimisation algorithm when benchmarked against a brute-force method.

Reverse Coding of a Common-Sense Physical Activity Intervention for Older Adults Using Elements of the Behaviour Change Wheel Framework.

"Common-sense" physical activity (PA) interventions for older adults may be more effective if developed in accordance with behavior change theory. One way to achieve this is through retrospectively applying a theoretical behavior change framework to "reverse code" an existing intervention and guide its ongoing development. This study aimed to detail a clear and systematic procedure that applied elements of the Behaviour Change Wheel (BCW) framework to reverse code the Active Ageing Pathway (AAP) intervention. The objectives of the procedure were to characterize the content of the AAP and its links to behavior change theory. The content of the AAP was first deconstructed through the examination of "standard operating procedures" documents, in-person observation, and a series of face-to-face discussions with AAP management. Then, the behavior change techniques (BCT) and BCW intervention functions associated with the AAP's content were identified and coded using the BCT Taxonomy version 1. Forty-one active components were identified within the AAP, which involved numerous professionals, and pertained to a diverse and interlinked range of factors, across various modes of delivery. The components were classified under 20 separate BCT labels, which related to eight of the nine BCW intervention functions. These outcomes were demonstrated to have practical applications for identifying gaps in intervention content as well as for guiding future intervention evaluation. This study supports previous work detailing the usefulness of reverse coding procedures as a tool for developing common-sense interventions, and is the first to do so in the context of a PA intervention for older adults.

Reverse Coding: a Proposed Alternative Methodology for Identifying Evidentiary Warrants

ABSTRACT This paper aims to critique approaches to qualitative coding that carry a bottom-up or inductive thinking. Despite the wide contributions of this epistemology to the social sciences, this paper contends that contemporary research and methodological debates have inadequately explored different epistemologies for coding. As such, this paper proposes and explores the concept of ‘reverse coding.’ In applying reverse coding to ethnographic data collected from observations of a multicultural language classroom, I demonstrate that reverse coding can explore intuitions or ‘hunches’ generated from the data that may not be supported by conventional qualitative coding. By finding such support through reverse coding, or the process of identifying preliminary propositions first and its constituent features afterward, this paper asserts that research employing multiple approaches to coding can extend its range of analysis to generate more robust findings.

Reversible cyclic codes over a class of chain rings and their application to DNA codes

Reversible cyclic codes over a class of chain rings and their application to DNA codes

Genetic Decompilation Concept of the Telecommunication Devices Machine Code

Reverse engineering correct source code from a machine code to find and neutralize vulnerabilities is the most pressing problem for the field of telecommunications equipment. The decompilation techniques applicable for this have potentially reached their evolutionary limit. As a result, new concepts are required that can make a quantum leap in problem solving. Proceeding from this, the paper proposes the concept of genetic decompilation, which is a solution to the problem of multiparameter optimization in the form of iterative approximation of instances of the source code to the "original" one which will compile to the given machine code. This concept is tested by conducting a series of experiments with the developed software prototype using a basic example of machine code. The results of the experiments prove the proof of the concept, thereby suggesting new innovative directions for ensuring information security in this subject area.

Multiwavelength magnetic coding of helical luminescence in ferromagnetic 2D layered CrI3

SummaryTwo-dimensional (2D) van der Waals (vdW) ferromagnets have opened new avenues for manipulating spin at the limits of single or few atomic layers, and for creating unique magneto-exciton devices through the coupling of ferromagnetic (FM) orders and excitons. However, 2D vdW ferromagnets explored so far have rarely possessed exciton behaviors; to date, FM CrI3 have been revealed to show ligand-field photoluminescence correlated with FM ordering, but typically with a broad emission peak. Here, we report a straightforward approach to realize strong coupling of narrow helical emission and FM orders in CrI3 through microsphere cavity. The resonant whispering-gallery modes (WGM) of SiO2 microspheres cause strong oscillation helical emissions with a full width at half-maximum (FWHM) of ∼5 nm under continuous wave excitation. Reversible magnetic coding of helical luminescence is realized in the range of 950–1100 nm. This work enables numerous opportunities for creating magnetic encoding lasing for photonic integrated chips.

Analyzing the code structures of multidimensional signals for a continuous information transmission channel

One of the directions to improve the efficiency of modern telecommunication systems is the transition to the use of multidimensional signals for continuous channels of information transmission. As a result of studies carried out in recent years, it has been established that it is possible to ensure high quality of information transmission in continuous channels by combining demodulation and decoding operations into a single procedure that involves the construction of a code construct for a multidimensional signal. This paper considers issues related to estimating the possibility to improve the efficiency of continuous information transmission channel by changing the signal distance of the code structure. It has been established that the code structures of such types as a hierarchical code construct of signals, a hierarchical code construct of signals with Euclidean metric, a reversible code construct of signals, a reversible code construct of signals with Euclidean metric have the potential, when used, to increase the speed of information transmission along a continuous channel. With a signal distance reduced by 10 percent or larger, it could increase by two times or faster. The estimation of the effect of reducing a signal distance on the efficiency of certain types of code structures was carried out. It has been established that the hierarchical reversible code construct, compared to the hierarchical code construct, provides a win of up to two or more times in the speed of information transmission with a halved signal distance. Implementing the modulation procedure has no fundamental difficulties, on the condition that for each code of the code construct the encoding procedure is known when using binary codes. The results reported here make it possible to build an acceptably complex demodulation procedure according to the specified types of code structures

An area-efficient, robust, and reversible QCA-based Hamming code generator, error detector, and corrector: design and performance estimation

An area-efficient, robust, and reversible QCA-based Hamming code generator, error detector, and corrector: design and performance estimation

Reversible cyclic codes over some finite rings and their application to DNA codes

Reversible cyclic codes over some finite rings and their application to DNA codes

True amplitude depth migration using curvelets

We have developed a true amplitude solution to the seismic imaging problem. We derive a diagonal scaling approach for the normal operator approximation in the curvelet domain. This is based on the theorem that states that curvelets remain approximately invariant under the action of the normal operator. We use curvelets as essential tools for approximation and inversion. We also exploit the theorem that states that the curvelet-domain approximation should be smooth in phase space by enforcing the smoothness of curvelet coefficients in the angle and space domains. We analyze our method using a reverse time migration-demigration code, simulating the acoustic wave equation on different synthetic models. Our method produces a good resolution with reflecting dips, reproduces the true amplitude reflectors, and compensates for incomplete illumination in seismic images.

Self dual, reversible and complementary duals constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4.

Abstract Over finite local Frobenius non-chain rings of length 5 and nilpotency index 4 and when the length of the code is relatively prime to the characteristic of the residue field of the ring, the structure of the dual of γ-constacyclic codes is established and the algebraic characterization of self-dual, reversible γ-constacyclic codes and γ-constacyclic codes with complementary dual are given.

On LCD codes over Z 4

Linear complementary dual(LCD) codes are being utilized to protect cryptographic implementations from side-channel and fault attacks. In this work, LCD codes over the ring Z 4 are examined. It is observed that an LCD cyclic code over Z 4 of odd length is always reversible. However, the converse of this result does not hold. A suitable example to validate this statement is presented. Further, a necessary and sufficient condition for a reversible cyclic code of odd length to be an LCD code is obtained. Finally, it is found that among cyclic codes of length 2 k , no non-trivial LCD code exists.