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Convolutional code with any code rate can be designed based on polynomial selection; however, in practice, a puncturing procedure is often used to achieve the required code rate. Puncturing is a technique used to make a m/n rate code from a "basic" low-rate (e.g., 1/n) code. It is achieved by deleting of some bits in the encoder output.
Reed–Muller codes are linear block codes that are locally testable, locally decodable, and list decodable. These properties make them particularly useful in the design of probabilistically checkable proofs . Traditional Reed–Muller codes are binary codes, which means that messages and codewords are binary strings.
The first element of a CIRC decoder is a relatively weak inner (32,28) Reed–Solomon code, shortened from a (255,251) code with 8-bit symbols. This code can correct up to 2 byte errors per 32-byte block. More importantly, it flags as erasures any uncorrectable blocks, i.e., blocks with more than 2 byte errors.
Pseudorandom noise. In cryptography, pseudorandom noise ( PRN [1]) is a signal similar to noise which satisfies one or more of the standard tests for statistical randomness. Although it seems to lack any definite pattern, pseudorandom noise consists of a deterministic sequence of pulses that will repeat itself after its period.
In linear algebra terms, the dual code is the annihilator of C with respect to the bilinear form . The dimension of C and its dual always add up to the length n : A generator matrix for the dual code is the parity-check matrix for the original code and vice versa. The dual of the dual code is always the original code.
Event generator. Event generators are software libraries that generate simulated high-energy particle physics events. [1] [2] They randomly generate events as those produced in particle accelerators, collider experiments or the early universe. Events come in different types called processes as discussed in the Automatic calculation of particle ...
Sine, square, triangle, and sawtooth waveforms. In electrical engineering, a function generator is usually a piece of electronic test equipment or software used to generate different types of electrical waveforms over a wide range of frequencies. Some of the most common waveforms produced by the function generator are the sine wave, square wave ...
Its generator polynomial as a cyclic code is given by. where is the set of quadratic residues of in the set and is a primitive th root of unity in some finite extension field of . The condition that is a quadratic residue of ensures that the coefficients of lie in . The dimension of the code is . Replacing by another primitive -th root of unity ...