Abstract: Aspects described herein may include detecting, by a browser extension, a checkout page for the purchase of an item using a credit card. Product transaction data and a warranty expiration date of the purchased item may be retrieved, and the warranty expiration date of the purchased item may be stored. Creation of a notification to be sent to the user prior to the warranty expiration may be scheduled. The notification, which includes the warranty expiration date of the purchased item, may then be forwarded to the user through the browser extension.

Abstract: Provided herein is a fast block circulant generated Hadamard matrix which is called jacket matrices of orders N=2p,4p,4kp,np, wherein k is a positive integer. The block Toeplitz circulant jacket matrices possess many properties of Walsh-Hadamard Toeplitz transform and also have the construction of block circulant, which can be applied to fast algorithms for decomposition easily. The matrix decomposition is of the form of the products of block identity I2 matrix and block Hadamard H2 matrix. The block Toeplitz circulant jacket matrices can be applied to the Kronecker MIMO channel.