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These examples also belong to the class of linear codes, and hence they are called linear block codes. More particularly, these codes are known as algebraic block codes, or cyclic block codes, because they can be generated using Boolean polynomials. Algebraic block codes are typically hard-decoded using algebraic decoders. [jargon]
Formally, a parity check matrix H of a linear code C is a generator matrix of the dual code, C ⊥. This means that a codeword c is in C if and only if the matrix-vector product Hc ⊤ = 0 (some authors [1] would write this in an equivalent form, cH ⊤ = 0.) The rows of a parity check matrix are the coefficients of the parity check equations. [2]
In coding theory, Hamming(7,4) is a linear error-correcting code that encodes four bits of data into seven bits by adding three parity bits. It is a member of a larger family of Hamming codes, but the term Hamming code often refers to this specific code that Richard W. Hamming introduced in 1950.
An (,) quasi-cyclic code is a linear block code such that, for some which is coprime to , the polynomial () is a codeword polynomial whenever () is a codeword polynomial. Here, codeword polynomial is an element of a linear code whose code words are polynomials that are divisible by a polynomial of shorter length called the generator polynomial .
jblas is a linear algebra library, created by Mikio Braun, for the Java programming language built upon BLAS and LAPACK. Unlike most other Java linear algebra libraries, jblas is designed to be used with native code through the Java Native Interface and comes with precompiled binaries. When used on one of the targeted architectures, it will ...
This is a decoder algorithm that efficiently corrects errors in Reed–Solomon codes for an RS(n, k), code based on the Reed Solomon original view where a message ,, is used as coefficients of a polynomial () or used with Lagrange interpolation to generate the polynomial () of degree < k for inputs ,, and then () is applied to +,, to create an ...
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EJML is free, written in 100% Java and has been released under an Apache v2.0 license. EJML has three distinct ways to interact with it: 1) Procedural, 2) SimpleMatrix, and 3) Equations. The procedural style provides all capabilities of EJML and almost complete control over matrix creation, speed, and specific algorithms.