For a linear code of length and dimension over , the code rate is . There are possible messages represented by codewords of length . More generally a block code has rate . This is a dimensionless redundancy measure, distinct from information transmitted per unit physical time.
The asymptotic rate-distance function is . It is the best asymptotic code rate available at the specified relative minimum distance. A limsup is used because the definition does not assume an ordinary limit exists.
// Target: algebra.bigb
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Code rate is a term commonly used in the context of coding theory and telecommunications to describe the efficiency of a code used for data transmission or storage. It is defined as the ratio of the number of information bits to the total number of bits transmitted or stored (which includes both information and redundancy bits).