Construction of I-Deletion-Correcting Ternary Codes

Finding large deletion correcting codes is an important issue in coding theory. Many researchers have studied this topic over the years. Varshamov and Tenegolts constructed the Varshamov-Tenengolts codes (VT codes) and Levenshtein showed the Varshamov-Tenengolts codes are perfect binary one-deletion correcting codes in 1992. Tenegolts constructed T codes to handle the non-binary cases. However the T codes are neither optimal nor perfect, which means some progress can be established. Latterly, Bours showed that perfect deletion-correcting codes have a close relationship with design theory. By this approach, Wang and Yin constructed perfect 5-deletion correcting codes of length 7 for large alphabet size. For our research, we focus on how to extend or combinatorially construct large codes with longer length, few deletions and small but non-binary alphabet especially ternary. After a brief study, we discovered some properties of T codes and produced some large codes by 3 different ways of extending some existing good codes.

New Bounds for the Maximum Size of Ternary Constant Weight Codes

This work was partially supported by the Bulgarian National Science Fund under Grant I–618/96.

Special subsets and optimum codes based on lattices and cosets

This paper introduces the concept of special subsets when applied to generator matrices based on lattices and cosets as presented by Calder-bank and Sloane. By using the special subsets we propose a non exhaustive code search for optimum codes. Although non exhaustive, the search always results in optimum codes for given (k1, V, Λ/Λ′). Tables with binary and ternary optimum codes to partitions of lattices with 8, 9 e 16 cosets, were obtained.

On the Error-Correcting Performance of some Binary and Ternary Linear Codes

In this work, we determine the coset weight spectra of all binary cyclic codes of lengths up to 33, ternary cyclic and negacyclic codes of lengths up to 20 and of some binary linear codes of lengths up to 33 which are distance-optimal, by using some of the algebraic properties of the codes and a computer assisted search. Having these weight spectra the monotony of the function of the undetected error probability after t-error correction P(t)ue (C,p) could be checked with any precision for a linear time. We have used a programm written in Maple to check the monotony of P(t)ue (C,p) for the investigated codes for a finite set of points of p € [0, p/(q-1)] and in this way to determine which of them are not proper.

Necessary and Sufficient Conditions for the Extendability of Ternary Linear Codes

We give the necessary and sufficient conditions for the extendability of ternary linear codes of dimension k ≥ 5 with minimum distance d ≡ 1 or 2 (mod 3) from a geometrical point of view.

Matrix-product codes over Fq

Codes C-1,...,C-M of length it over F-q and an M x N matrix A over F-q define a matrix-product code C = [C-1 (...) C-M] (.) A consisting of all matrix products [c(1) (...) c(M)] (.) A. This generalizes the (u/u + v)-, (u + v + w/2u + v/u)-, (a + x/b + x/a + b + x)-, (u + v/u - v)- etc. constructions. We study matrix-product codes using Linear Algebra. This provides a basis for a unified analysis of /C/, d(C), the minimum Hamming distance of C, and C-perpendicular to. It also reveals an interesting connection with MDS codes. We determine /C/ when A is non-singular. To underbound d(C), we need A to be 'non-singular by columns (NSC)'. We investigate NSC matrices. We show that Generalized Reed-Muller codes are iterative NSC matrix-product codes, generalizing the construction of Reed-Muller codes, as are the ternary 'Main Sequence codes'. We obtain a simpler proof of the minimum Hamming distance of such families of codes. If A is square and NSC, C-perpendicular to can be described using C-1(perpendicular to),...,C-M(perpendicular to) and a transformation of A. This yields d(C-perpendicular to). Finally we show that an NSC matrix-product code is a generalized concatenated code.

A formalized optimum code search for q-ary trellis codes

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The Nonexistence of [132, 6, 86]3 Codes and [135, 6, 88]3 Codes

We prove the nonexistence of [g3(6, d), 6, d]3 codes for d = 86, 87, 88, where g3(k, d) = ∑⌈d/3i⌉ and i=0 ... k−1. This determines n3(6, d) for d = 86, 87, 88, where nq(k, d) is the minimum length n for which an [n, k, d]q code exists.

Flat tori, lattices and bounds for commutative group codes

We show that commutative group spherical codes in R(n), as introduced by D. Slepian, are directly related to flat tori and quotients of lattices. As consequence of this view, we derive new results on the geometry of these codes and an upper bound for their cardinality in terms of minimum distance and the maximum center density of lattices and general spherical packings in the half dimension of the code. This bound is tight in the sense it can be arbitrarily approached in any dimension. Examples of this approach and a comparison of this bound with Union and Rankin bounds for general spherical codes is also presented.

Magnetization studies of binary and ternary Co-rich phases of the Co-Si-B system

CoB, CO(2)B, CoSi, Co(2)Si and CO(5)Si(2)B phases can be formed during heat-treatment of amorphous co-Si-B soft magnetic materials. Thus, it is important to determine their magnetic behavior as a function of applied field and temperature. In this study, polycrystalline single-phase samples of the above phases were produced via arc melting and heat-treatment under argon. The single-phase nature of the samples was confirmed via X-ray diffraction experiments. AC and DC magnetization measurements showed that Co(2)Si and CO(5)Si(2)B phases are paramagnetic. Minor amounts of either Co(2)Si or CoSi(2) in the CoSi-phase sample suggested a paramagnetic behavior of the CoSi-phase, however, it should be diamagnetic as shown in the literature. The diamagnetic behavior of the CoB phase was also confirmed. The paramagnetic behavior of CO(5)Si(2)B is for the first time reported. The magnetization results of the phase CO(2)B have a ferromagnetic signature already verified on previous NMR studies. A detailed set of magnetization measurements of this phase showed a change of the easy magnetization axis starting at 70K, with a temperature interval of about 13K at a very small field of 1 mT. As the strength of the field is increased the temperature interval is enlarged. The strength of field at which the magnetization saturates increases almost linearly as the temperature is increased above 70K. The room temperature total magnetostriction of the CO(2)B phase was determined to be 8 ppm at a field of 1T. (C) 2010 Elsevier B.V. All rights reserved.

Bidimensional codes recorded on an oxide glass surface using a continuous wave CO(2) laser

Surface heat treatment in glasses and ceramics, using CO(2) lasers, has attracted the attention of several researchers around the world due to its impact in technological applications, such as lab-on-a-chip devices, diffraction gratings and microlenses. Microlens fabrication on a glass surface has been studied mainly due to its importance in optical devices (fiber coupling, CCD signal enhancement, etc). The goal of this work is to present a systematic study of the conditions for microlens fabrications, along with the viability of using microlens arrays, recorded on the glass surface, as bidimensional codes for product identification. This would allow the production of codes without any residues (like the fine powder generated by laser ablation) and resistance to an aggressive environment, such as sterilization processes. The microlens arrays were fabricated using a continuous wave CO(2) laser, focused on the surface of flat commercial soda-lime silicate glass substrates. The fabrication conditions were studied based on laser power, heating time and microlens profiles. A He-Ne laser was used as a light source in a qualitative experiment to test the viability of using the microlenses as bidimensional codes.

Thermodynamic and topological instability approaches for forecasting glass-forming ability in the ternary Al-Ni-Y system

A thermodynamic approach to predict bulk glass-forming compositions in binary metallic systems was recently proposed. In this approach. the parameter gamma* = Delta H-amor/(Delta H-inter - Delta H-amor) indicates the glass-forming ability (GFA) from the standpoint of the driving force to form different competing phases, and Delta H-amor and Delta H-inter are the enthalpies for-lass and intermetallic formation, respectively. Good glass-forming compositions should have a large negative enthalpy for glass formation and a very small difference for intermetallic formation, thus making the glassy phase easily reachable even under low cooling rates. The gamma* parameter showed a good correlation with GFA experimental data in the Ni-Nb binary system. In this work, a simple extension of the gamma* parameter is applied in the ternary Al-Ni-Y system. The calculated gamma* isocontours in the ternary diagram are compared with experimental results of glass formation in that system. Despite sonic misfitting, the best glass formers are found quite close to the highest gamma* values, leading to the conclusion that this thermodynamic approach can lie extended to ternary systems, serving as a useful tool for the development of new glass-forming compositions. Finally the thermodynamic approach is compared with the topological instability criteria used to predict the thermal behavior of glassy Al alloys. (C) 2007 Elsevier B. V. All rights reserved.

Compatible Ternary Blends of Chitosan/poly(vinyl alcohol)/poly(lactic acid) Produced by Oil-in-Water Emulsion Processing

Ternary compatible blends of chitosan, poly(vinyl alcohol), and poly(lactic acid) were prepared by an oil-in-water (O/W) emulsion process. Solutions of chitosan in aqueous acetic acid, poly(vinyl alcohol) (PVA) in water, and poly(lactic acid) (PLA) in chloroform were blended with a high shear mixer. PVA was used as an emulsifier to stabilize the emulsion and to reduce the interfacial tension between the solid polymers in the blends-produced. It proved to work very well because the emulsions were stable for periods of days or weeks and compatible blends were obtained When PVA was added. This effect was attributed to a synergistic effect of PVA and chitosan because the binary blends PVA/PLA and chitosan/PLA were completely incompatible; The blends were characterized by scanning electron microscopy (SEM), differential scanning calorimetry (DSC), thermal mechanical analysis (TMA), stress strain tests, and Fourier transform infrared spectroscopy (FTIR). The results indicated that despite the fact that the system contained distinct phases some degree of molecular miscibility occurred when the three components were present in the blend.

One-time signature scheme from syndrome decoding over generic error-correcting codes

We describe a one-time signature scheme based on the hardness of the syndrome decoding problem, and prove it secure in the random oracle model. Our proposal can be instantiated on general linear error correcting codes, rather than restricted families like alternant codes for which a decoding trapdoor is known to exist. (C) 2010 Elsevier Inc. All rights reserved,

The study of ternary carbides formation during SPS consolidation process in the WC-Co-steel system

Tungsten carbide has a wide range of applications, mainly cemented carbides made of WC and Co, as wear resistant materials. However, the high cost of WC-Co powders encourages the use of a substrate to manufacture a functionally graded material (FGM) tool made of WC-Co and a tool steel. These materials join the high wear resistance of the cemented carbide and the toughness of the steel. This work deals with the study interaction of the WC-Co and H13 steel to design a functionally graded material by means of spark plasma sintering (SPS). The SPS, a novel sintering technique reaching the consolidation of the powders at relatively low temperatures and short dwell times, is a promising technique in processing materials. In this study, WC, H13 steel, WC-Co, WC-H13 steel and WC-Co-H13 steel bulk samples were investigated using scanning electron microscopy and X-ray diffraction techniques to evaluate the phase transformations involved during SPS consolidation process. The W(2)C and W(3)Fe(3)C precipitation were identified after the SPS consolidation of the WC and WC-H13 steel samples, respectively. The precipitation Of W(4)Co(2)C was also identified in the WC-Co and WC-Co-H13 steel samples. The WC-H 13 steel and WC-Co-H13 steel were also evaluated after heat treatments at 1100 degrees C for 9 h, which enhanced the chemical interaction and the precipitation of W(3)Fe(3)C and W(4)Co(2)C, respectively. (C) 2009 Elsevier Ltd. All rights reserved.