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.

0, 2, 120, 18624, 9876480, 20135116800, 163839423283200, 5348052945894113280, 699612285096273924587520, 366440137172271078986848665600, 768105432116827516249785005978419200, 6441762292785726797799215491828242028953600

Offset

1,2

Comments

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.

References

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

Links

Table of n, a(n) for n=1..12.

Formula

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

Mathematica

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

Crossrefs

Sequence in context: A362459 A077540 A272180 * A331500 A024343 A100043

Adjacent sequences: A187877 A187878 A187879 * A187881 A187882 A187883

Keyword

nonn,easy

Author

Ido Tal, Mar 14 2011

Status

approved