Coding theory

Block code

In coding theory, block codes are a large and important family of error-correcting codes that encode data in blocks.There is a vast number of examples for block codes, many of which have a wide range of practical applications. The abstract definition of block codes is conceptually useful because it allows coding theorists, mathematicians, and computer scientists to study the limitations of all block codes in a unified way.Such limitations often take the form of bounds that relate different parameters of the block code to each other, such as its rate and its ability to detect and correct errors. Examples of block codes are Reed–Solomon codes, Hamming codes, Hadamard codes, Expander codes, Golay codes, and Reed–Muller codes. 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. The term block code may also refer to any error-correcting code that acts on a block of bits of input data to produce bits of output data . Consequently, the block coder is a memoryless device. Under this definition codes such as turbo codes, terminated convolutional codes and other iteratively decodable codes (turbo-like codes) would also be considered block codes. A non-terminated convolutional encoder would be an example of a non-block (unframed) code, which has memory and is instead classified as a tree code. This article deals with "algebraic block codes". (Wikipedia).

Block code
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In this video, I calculate the determinant of a block matrix and show that the answer is what you expect, namely the product of the determinants of the blocks. This is useful for instance in the proof of the Cayley Hamilton theorem, but also in the theory of Jordan Forms. Cayley-Hamilton

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From playlist Compilation

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Related pages

Turbo code | Hamming weight | Kissing number | Communication channel | Channel capacity | Coding theory | Hamming distance | Finite field | Sphere packing | Hamming(7,4) | 24-cell | Linear code | Decoding methods | Rank error-correcting code | Hamming code | List decoding | Binary erasure channel | Information theory | Hadamard code | Reed–Muller code | Set (mathematics) | Binary Golay code | Shannon–Hartley theorem | Soft-decision decoder | Prime power | Expander code | String (computer science)