The formalism of quantum mechanics includes a rich collection of representations for describing quantum systems, including functions, graphs, matrices, histograms of probabilities, and Dirac notation. The varied features of these representations affect how computations are performed. For example, identifying probabilities of measurement outcomes…

Hill ciphers are linear codes that use as input a "plaintext" vector [p-right arrow above] of size n, which is encrypted with an invertible n x n matrix E to produce a "ciphertext" vector [c-right arrow above] = E [middle dot] [p-right arrow above]. Informally, a near-field is a triple [left angle bracket]N; +, *[right angle bracket] that…