Weight enumerators of Reed-Muller codes from cubic curves and their duals

Let $\mathbb{F}_q$ be a finite field of characteristic not equal to $2$ or $3$. We compute the weight enumerators of some projective and affine Reed-Muller codes of order $3$ over $\mathbb{F}_q$. These weight enumerators answer enumerative questions about plane cubic curves. We apply the MacWilliams theorem to give formulas for coefficients of the weight enumerator of the duals of these codes. We see how traces of Hecke operators acting on spaces of cusp forms for $\operatorname{SL}_2(\mathbb{Z})$ play a role in these formulas.Comment: 19 pages. To appear in "Arithmetic, Geometry, Cryptography, and Coding Theory" (Y. Aubry, E. W. Howe, C. Ritzenthaler, eds.), Contemp. Math., 201

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Reviews the creation and evolution of the Criminal Offender Record Information (CORI) system in Massachusetts, some of its key challenges, and ideas for reform

RWU Professor Writes Book on Personal Branding

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Teaching Stats for Data Science

“Data science” is a useful catchword for methods and concepts original to the field of statistics, but typically being applied to large, multivariate, observational records. Such datasets call for techniques not often part of an introduction to statistics: modeling, consideration of covariates, sophisticated visualization, and causal reasoning. This article re-imagines introductory statistics as an introduction to data science and proposes a sequence of 10 blocks that together compose a suitable course for extracting information from contemporary data. Recent extensions to the mosaic packages for R together with tools from the “tidyverse” provide a concise and readable notation for wrangling, visualization, model-building, and model interpretation: the fundamental computational tasks of data science