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Reed-Muller codes: An ideal theory approach. (English) Zbl 0868.94045
Summary: By using techniques from commutative algebra such as the ideal of a set of points, the \(a\)-invariant, the Hilbert function, and the Koszul complex, the main results about the Generalized and Projective Reed-Muller codes are obtained.

MSC:
94B05 Linear codes (general theory)
13D25 Complexes (MSC2000)
13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
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