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A187880 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. 2

%I

%S 0,2,120,18624,9876480,20135116800,163839423283200,

%T 5348052945894113280,699612285096273924587520,

%U 366440137172271078986848665600,768105432116827516249785005978419200,6441762292785726797799215491828242028953600

%N 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.

%C 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.

%D 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

%F a(n) = Product_{i=0..n-1} (2^n - 2^i) - n! * 2^(n*(n - 1)/2).

%t a[n_]:=Product[2^n - 2^i, {i, 0, n - 1}] - n!*2^(n*(n - 1)/2); Array[a,10]

%K nonn,easy

%O 1,2

%A _Ido Tal_, Mar 14 2011

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Last modified October 21 12:12 EDT 2019. Contains 328299 sequences. (Running on oeis4.)