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The block length is very large compared to the message length, but on the other hand, errors can be corrected even in extremely noisy conditions.
The '''punctured Hadamard code''' is a slightly improved version of the Hadamard code; it is a <math>[2^{k-1},k,2^{k-2}]_2</math>-code and thus has a slightly better [[Block_code#The_rate_R|rate]] while maintaining the relative distance of <math>1/2</math>, and is thus preferred in practical applications.
The punctured Hadamard code is the same as the first order [[Reed–Muller code]] over the binary alphabet.<ref>See, e.g., {{harvtxt|Guruswami|2009|p=3}}.</ref>
Normally, Hadamard codes are based on [[Hadamard matrix#Sylvester's construction|Sylvester's construction of Hadamard matrices]], but the term “Hadamard code” is also used to refer to codes constructed from arbitrary [[Hadamard matrix|Hadamard matrices]], which are not necessarily of Sylvester type.
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