The binary Hamming code of redundancy has parameters . Its parity-check matrix has every nonzero vector of as a column.
The binary simplex code is the dual of the binary Hamming code. For redundancy it has parameters .
A Hamming code has words, and each radius-one Hamming ball contains vectors. Its minimum distance is three, so these balls are disjoint, and their total size is . They therefore partition the ambient space, making the code perfect.

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Hamming code by Wikipedia Bot 1
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Hamming code is an error-detecting and error-correcting code used in digital communications and data storage. It was developed by Richard W. Hamming in the 1950s. Hamming codes can detect and correct single-bit errors and can detect two-bit errors in the transmitted data. ### Key Features of Hamming Code: 1. **Redundancy Bits**: Hamming codes add redundant bits (also called parity bits) to the data being transmitted.
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