Weight polarization and divisibility (Q751625)
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scientific article; zbMATH DE number 4176975
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weight polarization and divisibility |
scientific article; zbMATH DE number 4176975 |
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Weight polarization and divisibility (English)
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1990
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This paper develops the polarization of the weight function and presents a test for divisibility of a code that can be carried out on a given spanning set. The paper includes another proof of the theorem of \textit{J. Ax} [Am. J. Math. 86, 255--261 (1964; Zbl 0121.02003)] on divisors of weights of polynomial functions. The paper concludes with an application to Reed-Muller codes that leads to Ax's theorem.
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linear code
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divisibility test
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polarization
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weight function
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divisors of weights of polynomial functions
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Reed-Muller codes
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