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A187880
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Number of n X n matrices over GF(2) that can be used as a kernel to construct a polar code. That is, the number of matrices for which channel polarization occurs.
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2
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0, 2, 120, 18624, 9876480, 20135116800, 163839423283200, 5348052945894113280, 699612285096273924587520, 366440137172271078986848665600, 768105432116827516249785005978419200, 6441762292785726797799215491828242028953600
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OFFSET
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1,2
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COMMENTS
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An n X n matrix is polarizing if it is non-singular, and there is no permutation of its columns that results in an upper-triangular matrix.
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REFERENCES
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S. B. Korada, E. Sasoglu and R. Urbanke, Polar Codes: Characterization of Exponent, Bounds, and Constructions, IEEE Transactions on Information Theory, 56 (2010), 6253-6264
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LINKS
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FORMULA
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a(n) = Product_{i=0..n-1} (2^n - 2^i) - n! * 2^(n*(n - 1)/2).
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MATHEMATICA
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a[n_]:=Product[2^n - 2^i, {i, 0, n - 1}] - n!*2^(n*(n - 1)/2); Array[a, 10]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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