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Traditional Reed–Muller codes are binary codes, which means that messages and codewords are binary strings. When r and m are integers with 0 ≤ r ≤ m, the Reed–Muller code with parameters r and m is denoted as RM ( r , m ). When asked to encode a message consisting of k bits, where holds, the RM ( r , m) code produces a codeword ...
A generator matrix for a linear [,,]-code has format , where n is the length of a codeword, k is the number of information bits (the dimension of C as a vector subspace), d is the minimum distance of the code, and q is size of the finite field, that is, the number of symbols in the alphabet (thus, q = 2 indicates a binary code, etc.).
Theano is a Python library and optimizing compiler for manipulating and evaluating mathematical expressions, especially matrix-valued ones. [ 2] In Theano, computations are expressed using a NumPy -esque syntax and compiled to run efficiently on either CPU or GPU architectures.
The fern is one of the basic examples of self-similar sets, i.e. it is a mathematically generated pattern that can be reproducible at any magnification or reduction. Like the Sierpinski triangle , the Barnsley fern shows how graphically beautiful structures can be built from repetitive uses of mathematical formulas with computers.
Cross-platform. Type. Computer algebra system. License. New BSD License. Website. www .sympy .org. SymPy is an open-source Python library for symbolic computation. It provides computer algebra capabilities either as a standalone application, as a library to other applications, or live on the web as SymPy Live [ 2] or SymPy Gamma. [ 3]
Unless semantics of Python are changed, but in many cases speedup is possible with few or no changes in the Python code. The faster Julia source code can then be used from Python, or compiled to machine code, and based that way. Nuitka compiles Python into C. [162] Numba uses LLVM to compile a subset of Python to machine code.
The Hadamard code is a linear code, and all linear codes can be generated by a generator matrix .This is a matrix such that () = holds for all {,}, where the message is viewed as a row vector and the vector-matrix product is understood in the vector space over the finite field.
Convolutional code. In telecommunication, a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a data stream. The sliding application represents the 'convolution' of the encoder over the data, which gives rise to the term 'convolutional coding'.