Decoding and constructions of codes in rank and Hamming metric

As coding theory plays an important role in data transmission, decoding algorithms for new families of error correction codes are of great interest. This dissertation is dedicated to the decoding algorithms for new families of maximum rank distance (MRD) codes including additive generalized twisted Gabidulin (AGTG) codes and Trombetti-Zhou (TZ) codes, decoding algorithm for Gabidulin codes beyond half the minimum distance and also encoding and decoding algorithms for some new optimal rank metric codes with restrictions. We propose an interpolation-based decoding algorithm to decode AGTG codes where the decoding problem is reduced to the problem of solving a projective polynomial equation of the form q(x) = xqu+1 +bx+a = 0 for a,b ∈ Fqm. We investigate the zeros of q(x) when gcd(u,m)=1 and proposed a deterministic algorithm to solve a linearized polynomial equation which has a close connection to the zeros of q(x). An efficient polynomial-time decoding algorithm is proposed for TZ codes. The interpolation-based decoding approach transforms the decoding problem of TZ codes to the problem of solving a quadratic polynomial equation. Two new communication models are defined and using our models we manage to decode Gabidulin codes beyond half the minimum distance by one unit. Our models also allow us to improve the complexity for decoding GTG and AGTG codes. Besides working on MRD codes, we also work on restricted optimal rank metric codes including symmetric, alternating and Hermitian rank metric codes. Both encoding and decoding algorithms for these optimal families are proposed. In all the decoding algorithms presented in this thesis, the properties of Dickson matrix and the BM algorithm play crucial roles. We also touch two problems in Hamming metric. For the first problem, some cryptographic properties of Welch permutation polynomial are investigated and we use these properties to determine the weight distribution of a binary linear codes with few weights. For the second one, we introduce two new subfamilies for maximum weight spectrum codes with respect to their weight distribution and then we investigate their properties.Doktorgradsavhandlin

Encoding and decoding of several optimal rank metric codes

This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation encoding is the right choice for these codes and then we provide easily reversible encoding methods for each family. Later unique decoding algorithms for the codes are described. The decoding algorithms are interpolation-based and can uniquely correct errors for each code with rank up to ⌊(d − 1)/2⌋ in polynomial-time, where d is the minimum distance of the code.publishedVersio

On interpolation-based decoding of a class of maximum rank distance codes

In this paper we present an interpolation-based decoding algorithm to decode a family of maximum rank distance codes proposed recently by Trombetti and Zhou. We employ the properties of the Dickson matrix associated with a linearized polynomial with a given rank and the modified Berlekamp-Massey algorithm in decoding. When the rank of the error vector attains the unique decoding radius, the problem is converted to solving a quadratic polynomial, which ensures that the proposed decoding algorithm has polynomial-time complexity.acceptedVersio

The Study of Plasticized Amorphous Biopolymer Blend Electrolytes Based on Polyvinyl Alcohol (PVA): Chitosan with High Ion Conductivity for Energy Storage Electrical Double-Layer Capacitors (EDLC) Device Application

In this study, plasticized films of polyvinyl alcohol (PVA): chitosan (CS) based electrolyte impregnated with ammonium thiocyanate (NH4SCN) were successfully prepared using a solution-casting technique. The structural features of the electrolyte films were investigated through the X-ray diffraction (XRD) pattern. The enrichment of the amorphous phase with increasing glycerol concentration was confirmed by observing broad humps. The electrical impedance spectroscopy (EIS) portrays the improvement of ionic conductivity from 10−5 S/cm to 10−3 S/cm upon the addition of plasticizer. The electrolytes incorporated with 28 wt.% and 42 wt.% of glycerol were observed to be mainly ionic conductor as the ionic transference number measurement (TNM) was found to be 0.97 and 0.989, respectively. The linear sweep voltammetry (LSV) investigation indicates that the maximum conducting sample is stable up to 2 V. An electrolyte with the highest conductivity was used to make an energy storage electrical double-layer capacitor (EDLC) device. The cyclic voltammetry (CV) plot depicts no distinguishable peaks in the polarization curve, which means no redox reaction has occurred at the electrode/electrolyte interface. The fabricated EDLC displays the initial specific capacitance, equivalent series resistance, energy density, and power density of 35.5 F/g, 65 Ω, 4.9 Wh/kg, and 399 W/kg, respectively

Decoding and constructions of codes in rank and Hamming metric

As coding theory plays an important role in data transmission, decoding algorithms for new families of error correction codes are of great interest. This dissertation is dedicated to the decoding algorithms for new families of maximum rank distance (MRD) codes including additive generalized twisted Gabidulin (AGTG) codes and Trombetti-Zhou (TZ) codes, decoding algorithm for Gabidulin codes beyond half the minimum distance and also encoding and decoding algorithms for some new optimal rank metric codes with restrictions. We propose an interpolation-based decoding algorithm to decode AGTG codes where the decoding problem is reduced to the problem of solving a projective polynomial equation of the form q(x) = xqu+1 +bx+a = 0 for a,b ∈ Fqm. We investigate the zeros of q(x) when gcd(u,m)=1 and proposed a deterministic algorithm to solve a linearized polynomial equation which has a close connection to the zeros of q(x). An efficient polynomial-time decoding algorithm is proposed for TZ codes. The interpolation-based decoding approach transforms the decoding problem of TZ codes to the problem of solving a quadratic polynomial equation. Two new communication models are defined and using our models we manage to decode Gabidulin codes beyond half the minimum distance by one unit. Our models also allow us to improve the complexity for decoding GTG and AGTG codes. Besides working on MRD codes, we also work on restricted optimal rank metric codes including symmetric, alternating and Hermitian rank metric codes. Both encoding and decoding algorithms for these optimal families are proposed. In all the decoding algorithms presented in this thesis, the properties of Dickson matrix and the BM algorithm play crucial roles. We also touch two problems in Hamming metric. For the first problem, some cryptographic properties of Welch permutation polynomial are investigated and we use these properties to determine the weight distribution of a binary linear codes with few weights. For the second one, we introduce two new subfamilies for maximum weight spectrum codes with respect to their weight distribution and then we investigate their properties

On interpolation-based decoding of a class of maximum rank distance codes

In this paper we present an interpolation-based decoding algorithm to decode a family of maximum rank distance codes proposed recently by Trombetti and Zhou. We employ the properties of the Dickson matrix associated with a linearized polynomial with a given rank and the modified Berlekamp-Massey algorithm in decoding. When the rank of the error vector attains the unique decoding radius, the problem is converted to solving a quadratic polynomial, which ensures that the proposed decoding algorithm has polynomial-time complexity

The Anodic Behaviour of Bulk Copper in Ethaline and 1-Butyl-3-Methylimidazolium Chloride

The anodic dissolution of bulk metallic copper was conducted in ionic liquids (ILs)-a deep eutectic solvent (DES) ((CH3)3NC2H4OH) comprised of a 1:2 molar ratio mixture of choline chloride Cl (ChCl), and ethylene glycol (EG)-and imidazolium-based ILs, such as C4mimCl, using electrochemical techniques, such as cyclic voltammetry, anodic linear sweep voltammetry, and chronopotentiometry.To investigate the electrochemical dissolution mechanism, electrochemical impedance spectroscopy (EIS) was used. In addition to spectroscopic techniques, for instance, UV-visible spectroscopy, microscopic techniques, such as atomic force microscopy (AFM), were used. The significant industrial importance of metallic copper has motivated several research groups to deal with such an invaluable metal. It was confirmed that the speciation of dissolved copper from the bulk phase at the interface region is [CuCl3]- and [CuCl4]2- in such chloride-rich media, and the EG determine the structure of the interfacial region in the electrochemical dissolution process. A super-saturated solution was produced at the electrode/solution interface and CuCl2 was deposited on the metal surface. © 2019 by the authors

Structural and Optical Characteristics of PVA:C-Dot Composites: Tuning the Absorption of Ultra Violet (UV) Region

In this work the influence of carbon nano-dots (CNDs) on absorption of ultra violet (UV) spectra in hybrid PVA based composites was studied. The FTIR results reveal the complex formation between PVA and CNDs. The shifting was observed in XRD spectrum of PVA:CNDs composites compared to pure PVA. The Debye-Scherrer formula was used to calculate the crystallite size of CNDs and crystalline phases of pure PVA and PVA:CNDs composites. The FESEM images emphasized the presence and dispersion of C-dots on the surface of the composite samples. From the images, a strong and clear absorption was noticed in the spectra. The strong absorption that appeared peaks at 280 nm and 430 nm can be ascribed to the n-π* and π-π* transitions, respectively. The absorption edge shifted to lower photon energy sides with increasing CNDs. The luminescence behavior of PVA:CNDs composite was confirmed using digital and photo luminescence (PL) measurements. The optical dielectric constant which is related to the density of states was studied and the optical band gap was characterized accurately using optical dielectric loss parameter. The Taucs model was used to determine the type of electronic transition in the samples

An Investigation into the PVA:MC:NH4Cl-Based Proton-Conducting Polymer-Blend Electrolytes for Electrochemical Double Layer Capacitor (EDLC) Device Application: The FTIR, Circuit Design and Electrochemical Studies

In this report, the preparation of solid polymer electrolytes (SPEs) is performed from polyvinyl alcohol, methyl cellulose (PVA-MC), and ammonium chloride (NH4Cl) using solution casting methodology for its use in electrical double layer capacitors (EDLCs). The characterizations of the prepared electrolyte are conducted using a variety of techniques, including Fourier transform infrared spectroscopy (FTIR), electrical impedance spectroscopy (EIS), cyclic voltammetry (CV), and linear sweep voltammetry (LSV). The interaction between the polymers and NH4Cl salt are assured via FTIR. EIS confirms the possibility of obtaining a reasonably high conductance of the electrolyte of 1.99 × 10−3 S/cm at room temperature. The dielectric response technique is applied to determine the extent of the ion dissociation of the NH4Cl in the PVA-MC-NH4Cl systems. The appearance of a peak in the imaginary part of the modulus study recognizes the contribution of chain dynamics and ion mobility. Transference number measurement (TNM) is specified and is found to be (tion) = 0.933 for the uppermost conducting sample. This verifies that ions are the predominant charge carriers. From the LSV study, 1.4 V are recorded for the relatively high-conducting sample. The CV curve response is far from the rectangular shape. The maximum specific capacitance of 20.6 F/g is recorded at 10 mV/s