Reed-Muller Code

A binary Reed-Muller code is the linear code formed by evaluating all multilinear polynomials of degree at most over the finite field at all points of , where . Its codewords have length . In particular, consists of the evaluation vectors of affine Boolean functions.

Wang et al. (2026) proved that the code covering radius of is 242. This is the greatest Hamming distance from a nine-variable Boolean function to the nearest affine Boolean function.

See also

Boolean Function, Boolean Function Nonlinearity, Code Covering Radius, Error-Correcting Code, Linear Code

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References

Wang, Q.; Lou, Y.; and Wang, Z. "The Covering Radius of the Reed-Muller Code

Is 242." 13 Oct 2026. https://arxiv.org/abs/2610.17871.

Cite this as:

Weisstein, Eric W. "Reed-Muller Code." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Reed-MullerCode.html

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