Limited-Magnitude Error-Correcting Gray Codes for Rank Modulation

We construct Gray codes over permutations for the rank-modulation scheme, which are also capable of correcting errors under the infinity-metric. These errors model limited-magnitude or spike errors, for which only single-error-detecting Gray codes are currently known. Surprisingly, the error-correcting codes we construct achieve a better asymptotic rate than that of presently known constructions not having the Gray property, and exceed the Gilbert-Varshamov bound. Additionally, we present efficient ranking and unranking procedures, as well as a decoding procedure that runs in linear time. Finally, we also apply our methods to solve an outstanding issue with error-detecting rank-modulation Gray codes (snake-in-the-box codes) under a different metric, the Kendall $\tau$-metric, in the group of permutations over an even number of elements $S_{2n}$, where we provide asymptotically optimal codes.Comment: Revised version for journal submission. Additional results include more tight auxiliary constructions, a decoding shcema, ranking/unranking procedures, and application to snake-in-the-box codes under the Kendall tau-metri

2017 Annual Research Symposium Abstract Book

2017 annual volume of abstracts for science research projects conducted by students at Trinity College

Science Requirements and Conceptual Design for a Polarized Medium Energy Electron-Ion Collider at Jefferson Lab

This report presents a brief summary of the science opportunities and program of a polarized medium energy electron-ion collider at Jefferson Lab and a comprehensive description of the conceptual design of such a collider based on the CEBAF electron accelerator facility.Comment: 160 pages, ~93 figures This work was supported by the U.S. Department of Energy, Office of Nuclear Physics, under Contract No. DE-AC05-06OR23177, DE-AC02-06CH11357, DE-AC05-060R23177, and DESC0005823. The U.S. Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce this manuscript for U.S. Government purpose