Block code in the context of Reed–Solomon code

Block code in the context of Reed–Solomon code

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⭐ Core Definition: 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, Reed–Muller codes and Polar 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.

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Block code in the context of Hamming distance

In information theory, the Hamming distance between two strings or vectors of equal length is the number of positions at which the corresponding symbols are different. In other words, it measures the minimum number of substitutions required to change one string into the other, or equivalently, the minimum number of errors that could have transformed one string into the other. In a more general context, the Hamming distance is one of several string metrics for measuring the edit distance between two sequences. It is named after the American mathematician Richard Hamming.

A major application is in coding theory, more specifically to block codes, in which the equal-length strings are vectors over a finite field.

View the full Wikipedia page for Hamming distance
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Coding theory → Channel coding → Mathematician → Computer scientist → Reed–Solomon code → Hamming code → Hadamard code → Expander code → Golay code (disambiguation) → Reed–Muller code → Polar code (coding theory) → Linear code →