| Some applications of the Discrete Fourier Transform (DFT) in coding and in cryptography are described. The DFT over general commutative rings is introduced and the condition for its existence given. Blahut's Theorem, which relates the DFT to linear complexity, is shown to hold unchanged in general commutative rings. I. The (Usual) Discrete Fourier Transform Let be a primitive N th root of uni...

Unique Mapped Real Transform (UMRT) is a transform which helps in frequency domain analysis of signals in the real domain. Different algorithms are developed for the computation of the unique MRT coefficients for N a power of 2 and for N an even number. They identify and place the UMRT coefficients in the form of an N N UMRT matrix. The basis matrices of this transform are observed to be spars...

The Burrows Wheeler transform has applications in data compression as well as full text indexing. Despite its important applications and various existing algorithmic approaches the construction of the transform for large data sets is still challenging. In this paper we present a new semi external memory algorithm capable of constructing the transform in time O(n log2 log n) on average if su cie...

A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum algorithms. We present a divide-and-conquer approach to the design of various quantum algorithms. The class of algorithm includes many transforms which are well-k...