The largest minimum weight of a self-dual doubly-even binary (n, k, d) code is d = 4 n/24 + 4. Of such codes with length divisible by 24, the Golay Code is the only (24, 12, 8) code, the Extended Quadratic Residue Code is the only known (48, 24, 12) code, and there is no known (72, 36, 16) code. One may partition the search for a (48, 24, 12) self-dual doubly-even code into 3 cases. A previous search assuming one of the cases found only the Extended Quadratic Residue Code. In this paper we examine the remaining 2 cases. Separate searches assuming each of the remaining cases found no codes and thus the Extended Quadratic Residue Code is the only doubly-even self-dual (48, 24, 12) code.

Alzheimer's disease (AD) is an irreversible, progressive neurological disorder that causes memory and thinking skill loss. Many different methods and algorithms have been applied to extract patterns from neuroimaging data in order to distinguish different stages of Alzheimer's disease (AD). However, the similarity of the brain patterns in older adults and in different stages makes the classification of different stages a challenge for researchers.In this paper, convolutional neuronal network architecture AlexNet was applied to fMRI datasets to classify different stages of the disease. We classified five different stages of Alzheimer's using a deep learning algorithm. The method successfully classified normal healthy control (NC), significant memory concern (SMC), early mild cognitive impair (EMCI), late cognitive mild impair (LMCI), and Alzheimer's disease (AD). The model was implemented using GPU high performance computing. Before applying any classification, the fMRI data were strictly preprocessed. Then, low to high level features were extracted and learned using the AlexNet model. Our experiments show significant improvement in classification. The average accuracy of the model was 97.63%. We then tested our model on test datasets to evaluate the accuracy of the model per class, obtaining an accuracy of 94.97% for AD, 95.64% for EMCI, 95.89% for LMCI, 98.34% for NC, and 94.55% for SMC.

Parkinson's disease (PD) is a degenerative disorder of the central nervous system that has many debilitating symptoms which affect the patient's motor system and can cause significant changes in their gait. By using genetic programming, we aim to develop descriptive symbolic nonlinear models of PD patient gait from time series data recorded from pressure sensors under subjects' feet. When compared to popular types of linear regression (OLS and LASSO), the nonlinear models fit their data better and generalize to unseen data significantly better. It was found that models developed for healthy control subjects generalized to other control subjects well, however the models trained on subjects with PD did not generalize well to other PD patients, which complicates the issue of being able to detect the progression of the disease. It is suspected that health care professionals can have difficulty classifying PD due to a lack of accurate data from patient reports; having individually trained models for active monitoring of patients would help in effectively diagnosing PD.

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