Applications of finite geometries to designs and codes

This dissertation concerns the intersection of three areas of discrete mathematics: finite geometries, design theory, and coding theory. The central theme is the power of finite geometry designs, which are constructed from the points and t-dimensional subspaces of a projective or affine geometry. We use these designs to construct and analyze combinatorial objects which inherit their best properties from these geometric structures. A central question in the study of finite geometry designs is Hamada’s conjecture, which proposes that finite geometry designs are the unique designs with minimum p-rank among all designs with the same parameters. In this dissertation, we will examine several questions related to Hamada’s conjecture, including the existence of counterexamples. We will also study the applicability of certain decoding methods to known counterexamples. We begin by constructing an infinite family of counterexamples to Hamada’s conjecture. These designs are the first infinite class of counterexamples for the affine case of Hamada’s conjecture. We further demonstrate how these designs, along with the projective polarity designs of Jungnickel and Tonchev, admit majority-logic decoding schemes. The codes obtained from these polarity designs attain error-correcting performance which is, in certain cases, equal to that of the finite geometry designs from which they are derived. This further demonstrates the highly geometric structure maintained by these designs. Finite geometries also help us construct several types of quantum error-correcting codes. We use relatives of finite geometry designs to construct infinite families of q-ary quantum stabilizer codes. We also construct entanglement-assisted quantum error-correcting codes (EAQECCs) which admit a particularly efficient and effective error-correcting scheme, while also providing the first general method for constructing these quantum codes with known parameters and desirable properties. Finite geometry designs are used to give exceptional examples of these codes.

Moving Beyond Hastiness and Superficiality: Being an Ethical Technical Communicator via Digital Communication Technologies in Health Care

This thesis examines digital technologies used by technical communicators in healthcare settings. I show that technical communicators, who function as users, advocators and evaluators, need a useable framework for ethical engagement with digital technologies, which integrally affect the physician-patient relationship. Therefore, I apply rhetorical methodology by producing useable knowledge and phenomenological methodology by examining lived experiences of technical communicators. Substantiation comes from theories spanning technical communication, philosophy, and composition studies. Evidence also emerges from qualitative interviews with communication professionals working in healthcare; my concerns arise from personal experiences with electronic recordkeeping in the exam room. This thesis anticipates challenging the presumed theory-practice divide while encouraging greater disciplinary reciprocity. Because technical communication infuses theory into productive capacity, this thesis presents the tripartite summons of the ethical technical communicator: to exercise critically-reflective action that safeguards the physician-patient relationship by ways of using digital technologies, advocating for audiences, and evaluating digital technologies.

A STUDY ON THE FEASIBILITY OF UNIVERSAL CHIP CONTROL IN MACHINING

A novel solution to the long standing issue of chip entanglement and breakage in metal cutting is presented in this dissertation. Through this work, an attempt is made to achieve universal chip control in machining by using chip guidance and subsequent breakage by backward bending (tensile loading of the chip's rough top surface) to effectively control long continuous chips into small segments. One big limitation of using chip breaker geometries in disposable carbide inserts is that the application range is limited to a narrow band depending on cutting conditions. Even within a recommended operating range, chip breakers do not function effectively as designed due to the inherent variations of the cutting process. Moreover, for a particular process, matching the chip breaker geometry with the right cutting conditions to achieve effective chip control is a very iterative process. The existence of a large variety of proprietary chip breaker designs further exacerbates the problem of easily implementing a robust and comprehensive chip control technique. To address the need for a robust and universal chip control technique, a new method is proposed in this work. By using a single tool top form geometry coupled with a tooling system for inducing chip breaking by backward bending, the proposed method achieves comprehensive chip control over a wide range of cutting conditions. A geometry based model is developed to predict a variable edge inclination angle that guides the chip flow to a predetermined target location. Chip kinematics for the new tool geometry is examined via photographic evidence from experimental cutting trials. Both qualitative and quantitative methods are used to characterize the chip kinematics. Results from the chip characterization studies indicate that the chip flow and final form show a remarkable consistency across multiple levels of workpiece and tool configurations as well as cutting conditions. A new tooling system is then designed to comprehensively break the chip by backward bending. Test results with the new tooling system prove that by utilizing the chip guidance and backward bending mechanism, long continuous chips can be more consistently broken into smaller segments that are generally deemed acceptable or good chips. It is found that the proposed tool can be applied effectively over a wider range of cutting conditions than present chip breakers thus taking possibly the first step towards achieving universal chip control in machining.

QUANTUM CORRELATIONS OF LIGHTS IN MACROSCOPIC ENVIRONMENTS

This dissertation presents a detailed study in exploring quantum correlations of lights in macroscopic environments. We have explored quantum correlations of single photons, weak coherent states, and polarization-correlated/polarization-entangled photons in macroscopic environments. These included macroscopic mirrors, macroscopic photon number, spatially separated observers, noisy photons source and propagation medium with loss or disturbances. We proposed a measurement scheme for observing quantum correlations and entanglement in the spatial properties of two macroscopic mirrors using single photons spatial compass state. We explored the phase space distribution features of spatial compass states, such as chessboard pattern by using the Wigner function. The displacement and tilt correlations of the two mirrors were manifested through the propensities of the compass states. This technique can be used to extract Einstein-Podolsky-Rosen correlations (EPR) of the two mirrors. We then formulated the discrete-like property of the propensity Pb(m,n), which can be used to explore environmental perturbed quantum jumps of the EPR correlations in phase space. With single photons spatial compass state, the variances in position and momentum are much smaller than standard quantum limit when using a Gaussian TEM00 beam. We observed intrinsic quantum correlations of weak coherent states between two parties through balanced homodyne detection. Our scheme can be used as a supplement to decoy-state BB84 protocol and differential phase-shift QKD protocol. We prepared four types of bipartite correlations ±cos2(θ12) that shared between two parties. We also demonstrated bits correlations between two parties separated by 10 km optical fiber. The bits information will be protected by the large quantum phase fluctuation of weak coherent states, adding another physical layer of security to these protocols for quantum key distribution. Using 10 m of highly nonlinear fiber (HNLF) at 77 K, we observed coincidence to accidental-coincidence ratio of 130±5 for correlated photon-pair and Two-Photon Interference visibility >98% entangled photon-pair. We also verified the non-local behavior of polarization-entangled photon pair by violating Clauser-Horne-Shimony-Holt Bell’s inequality by more than 12 standard deviations. With the HNLF at 300 K (77 K), photon-pair production rate about factor 3(2) higher than a 300 m dispersion-shifted fiber is observed. Then, we studied quantum correlation and interference of photon-pairs; with one photon of the photon-air experiencing multiple scattering in a random medium. We observed that depolarization noise photon in multiple scattering degrading the purity of photon-pair, and the existence of Raman noise photon in a photon-pair source will contribute to the depolarization affect. We found that quantum correlation of polarization-entangled photon-pair is better preserved than polarization-correlated photon-pair as one photon of the photon-pair scattered through a random medium. Our findings showed that high purity polarization-entangled photon-pair is better candidate for long distance quantum key distribution.