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<?php
include "page_template.html"
?>
<div id="temp-content" style="display: none;">
<h3>The Nordstrom-Robinson code</h3>
<hr>
<br>
<pre>
<code class="magma">
//////////////////////////////////////////////////////////////////////////////
// Work done by PHD student Emanuele Bellini, //
// University of Trento, 2014. //
// Emanuele Bellini, 2014 //
//////////////////////////////////////////////////////////////////////////////
intrinsic NordstromRobinsonCode() -> ModMatFldElt
{
Return the Nordstrom-Robinson code in the form of a binary 16x256 matrix.
}
/*
From: Huffman-Pless, "Fundamentals of Error Correcting Codes",
2.3.4 - The Nordstrom–Robinson code
The existence of the Nordstrom–Robinson code shows that
A_2(16,6) = 256.
TO USE IT:
NRC := NordstromRobinsonCode() ;
To check the minimum distance is 6:
min := 16 ;
for i in [1..Nrows(NRC)] do
for j in [i+1..Nrows(NRC)-1] do
if Weight(NRC[i] + NRC[j]) lt min then
min := Weight(NRC[i] + NRC[j]) ;
end if ;
end for ;
end for ;
*/
local C ; // Extended Golay code
local G ; // Generator matrix of C
local v ; // vector of 24 bits
local CT ; // subcode of C of 32 codewords with 0 in the first 8 components
local c ; // list of 8 special codewords to create the cosets of CT
local CC ; // list of 8 cosets of CT
local N ; // concatenation of the cosets CC[i] (256 codewords of length 24)
local N16 ; // Nordstrom-Robinson code:
// - punturing of N in the first 8 components
// - 256 codewords
// - length 16
// - distance 6
/////////
// STEP 1 - Let C be the [24, 12, 8] extended binary Golay code
/////////
C := GolayCode(GF(2),true) ;
/*
[24, 12, 8] "Extended Golay Code" Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1]
[0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 1]
[0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0]
[0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1]
[0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1]
[0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 1]
*/
/////////
// STEP 2 - Let C be the [24, 12, 8] extended binary Golay code
// chosen to contain the weight 8 codeword c = 11...100...0
/////////
G := GeneratorMatrix(C) ;
/*
G;
[1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1]
[0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 1]
[0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0]
[0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1]
[0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1]
[0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 1]
*/
G := SwapColumns(G,2,13) ;
G := SwapColumns(G,3,15) ;
G := SwapColumns(G,4,17) ;
G := SwapColumns(G,5,18) ;
G := SwapColumns(G,6,19) ;
G := SwapColumns(G,7,23) ;
G := SwapColumns(G,8,24) ;
/*
G;
[1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 1 1 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0]
[0 1 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0]
[0 1 0 0 1 1 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0]
[0 1 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0]
[0 0 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0]
[0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0]
[0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1]
[0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 1 1 1 0 0]
[0 0 1 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0]
[0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0]
[0 0 0 1 1 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0]
*/
C := LinearCode(G) ;
v := Vector(GF(2),[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]) ;
/*
v;
(1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0)
v in C ;
true
*/
/////////
// STEP 3 - Let C(T) be the subcode of C which is zero on T
// (T is the set consisting of the first eight coordinates)
/////////
CT := [] ;
i := 1 ;
for c in C do
if c[1] eq 0 and
c[2] eq 0 and
c[3] eq 0 and
c[4] eq 0 and
c[5] eq 0 and
c[6] eq 0 and
c[7] eq 0 and
c[8] eq 0 then
CT[i] := c ;
i := i + 1 ;
end if ;
end for ;
/*
CT;
[
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
(0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0),
(0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0),
(0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 1 1 1 0 0),
(0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 1 1 1 1),
(0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1),
(0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 1),
(0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 1),
(0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 0 0),
(0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 1 0 1 1 0 1 0),
(0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 1 0 0 1 1 0),
(0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 0),
(0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 1 1),
(0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 0 0 1 0 1),
(0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 1 1 0 0 1),
(0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1),
(0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 0),
(0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 0 0 0 0 0),
(0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 0 0 1 1 1 0 0),
(0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 1 0 1 0 1 0),
(0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 0 1 0 0 1),
(0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1),
(0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 0 0 0 1 1),
(0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 1 0 1),
(0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 1 1 0 1 0),
(0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 1 0 0 1 1 0 0),
(0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 1 1 0 0 0 0),
(0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0),
(0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 1),
(0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1),
(0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 1),
(0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 0 1)
]
*/
/////////
// STEP 4 - construct c[i] in C
// - c[0] = (0 ... 0 )
// - for 1 <= i <= 7 let
// c[i] = a codeword of C with zeros in the first eight coordinates
// except coordinate i and coordinate 8
/////////
c := [] ;
for i in [1..7] do
for x in C do
if x[i] eq 1 and
x[8] eq 1 and
IntegerRing()!(x[1]) +
IntegerRing()!(x[2]) +
IntegerRing()!(x[3]) +
IntegerRing()!(x[4]) +
IntegerRing()!(x[5]) +
IntegerRing()!(x[6]) +
IntegerRing()!(x[7]) +
IntegerRing()!(x[8]) eq 2 then
c[i] := x ;
end if ;
end for ;
end for ;
c[8] := ZeroMatrix(GF(2),1,24)[1] ;
/*
c;
[
(1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 1 1),
(0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0),
(0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 0),
(0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 1 0 1 0 0 0),
(0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 1 0 1),
(0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0),
(0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1)
]
*/
/////////
// STEP 5 - let CC[j] j be the coset c[j] + CT
// of CT in the extended Golay code C
// For 0 <= j <= 7
/////////
CC := [] ;
for j in [1..8] do
CC[j] := [] ;
for i in [1..#CT] do
CC[j][i] := CT[i] + c[j] ;
end for ;
end for ;
/////////
// STEP 6 - Let N be the union of the eight cosets CC[1], ..., CC[8]
/////////
N := CC[1] cat CC[2] cat CC[3] cat CC[4] cat
CC[5] cat CC[6] cat CC[7] cat CC[8] ;
/////////
// STEP 7 - The Nordstrom–Robinson code N16
// is the code obtained by puncturing N on T
// (set consisting of the first eight coordinates)
/////////
N16 := [] ;
for i in [1..#N] do
N16[i] := ZeroMatrix(GF(2),1,16)[1] ;
for j in [1..Ncols(N[i])-8] do
N16[i][j] := N[i][j+8] ;
end for ;
end for ;
/*
#N16 ;
256
N16 ;
[
(0 0 0 0 1 0 1 0 0 0 0 1 0 1 1 1),
(1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1),
(1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1),
(0 1 0 0 1 1 1 0 1 1 1 0 1 0 1 1),
(0 1 1 0 1 0 1 1 0 0 0 0 1 0 0 0),
(1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 0),
(1 0 1 0 1 1 0 0 1 0 0 0 0 0 1 0),
(0 0 1 0 1 1 1 1 1 1 1 1 0 1 0 0),
(0 0 1 1 1 1 0 1 0 0 1 1 1 0 1 1),
(1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 1),
(1 1 1 1 1 0 1 0 1 0 1 1 0 0 0 1),
(0 1 1 1 1 0 0 1 1 1 0 0 0 1 1 1),
(0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0),
(1 1 0 1 1 1 1 1 0 1 0 1 0 0 1 0),
(1 0 0 1 1 0 1 1 1 0 1 0 1 1 1 0),
(0 0 0 1 1 0 0 0 1 1 0 1 1 0 0 0),
(0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 1),
(1 0 0 1 0 1 0 0 1 1 1 1 0 1 1 1),
(1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1),
(0 1 0 1 0 0 1 1 0 1 1 1 1 1 0 1),
(0 1 1 1 0 1 1 0 1 0 0 1 1 1 1 0),
(1 1 1 1 0 1 0 1 1 1 1 0 1 0 0 0),
(1 0 1 1 0 0 0 1 0 0 0 1 0 1 0 0),
(0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 0),
(0 0 1 0 0 0 0 0 1 0 1 0 1 1 0 1),
(1 0 1 0 0 0 1 1 1 1 0 1 1 0 1 1),
(1 1 1 0 0 1 1 1 0 0 1 0 0 1 1 1),
(0 1 1 0 0 1 0 0 0 1 0 1 0 0 0 1),
(0 1 0 0 0 0 0 1 1 0 1 1 0 0 1 0),
(1 1 0 0 0 0 1 0 1 1 0 0 0 1 0 0),
(1 0 0 0 0 1 1 0 0 0 1 1 1 0 0 0),
(0 0 0 0 0 1 0 1 0 1 0 0 1 1 1 0),
(0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0),
(1 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0),
(1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0),
(0 1 0 0 1 1 1 0 1 0 0 1 0 0 0 0),
(0 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1),
(1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1),
(1 0 1 0 1 1 0 0 1 1 1 1 1 0 0 1),
(0 0 1 0 1 1 1 1 1 0 0 0 1 1 1 1),
(0 0 1 1 1 1 0 1 0 1 0 0 0 0 0 0),
(1 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0),
(1 1 1 1 1 0 1 0 1 1 0 0 1 0 1 0),
(0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0),
(0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1),
(1 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1),
(1 0 0 1 1 0 1 1 1 1 0 1 0 1 0 1),
(0 0 0 1 1 0 0 0 1 0 1 0 0 0 1 1),
(0 0 0 1 0 1 1 1 1 1 1 1 1 0 1 0),
(1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0),
(1 1 0 1 0 0 0 0 0 1 1 1 0 0 0 0),
(0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0),
(0 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1),
(1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1),
(1 0 1 1 0 0 0 1 0 1 1 0 1 1 1 1),
(0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 1),
(0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0),
(1 0 1 0 0 0 1 1 1 0 1 0 0 0 0 0),
(1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 0),
(0 1 1 0 0 1 0 0 0 0 1 0 1 0 1 0),
(0 1 0 0 0 0 0 1 1 1 0 0 1 0 0 1),
(1 1 0 0 0 0 1 0 1 0 1 1 1 1 1 1),
(1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 1),
(0 0 0 0 0 1 0 1 0 0 1 1 0 1 0 1),
(0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 0),
(1 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0),
(1 1 0 0 1 0 1 1 1 1 1 1 1 0 0 0),
(0 1 0 0 1 0 0 0 1 0 0 0 1 1 1 0),
(0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1),
(1 1 1 0 1 1 1 0 0 0 0 1 1 0 1 1),
(1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1),
(0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1),
(0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0),
(1 0 1 1 1 0 0 0 0 0 1 0 1 0 0 0),
(1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 0),
(0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0),
(0 1 0 1 1 0 1 0 0 1 0 0 0 0 0 1),
(1 1 0 1 1 0 0 1 0 0 1 1 0 1 1 1),
(1 0 0 1 1 1 0 1 1 1 0 0 1 0 1 1),
(0 0 0 1 1 1 1 0 1 0 1 1 1 1 0 1),
(0 0 0 1 0 0 0 1 1 1 1 0 0 1 0 0),
(1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0),
(1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 0),
(0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0),
(0 1 1 1 0 0 0 0 1 1 1 1 1 0 1 1),
(1 1 1 1 0 0 1 1 1 0 0 0 1 1 0 1),
(1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 1),
(0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1),
(0 0 1 0 0 1 1 0 1 1 0 0 1 0 0 0),
(1 0 1 0 0 1 0 1 1 0 1 1 1 1 1 0),
(1 1 1 0 0 0 0 1 0 1 0 0 0 0 1 0),
(0 1 1 0 0 0 1 0 0 0 1 1 0 1 0 0),
(0 1 0 0 0 1 1 1 1 1 0 1 0 1 1 1),
(1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1),
(1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1),
(0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 1),
(0 0 0 0 1 1 0 1 1 0 1 0 1 0 0 0),
(1 0 0 0 1 1 1 0 1 1 0 1 1 1 1 0),
(1 1 0 0 1 0 1 0 0 0 1 0 0 0 1 0),
(0 1 0 0 1 0 0 1 0 1 0 1 0 1 0 0),
(0 1 1 0 1 1 0 0 1 0 1 1 0 1 1 1),
(1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 1),
(1 0 1 0 1 0 1 1 0 0 1 1 1 1 0 1),
(0 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1),
(0 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0),
(1 0 1 1 1 0 0 1 1 1 1 1 0 0 1 0),
(1 1 1 1 1 1 0 1 0 0 0 0 1 1 1 0),
(0 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0),
(0 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1),
(1 1 0 1 1 0 0 0 1 1 1 0 1 1 0 1),
(1 0 0 1 1 1 0 0 0 0 0 1 0 0 0 1),
(0 0 0 1 1 1 1 1 0 1 1 0 0 1 1 1),
(0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0),
(1 0 0 1 0 0 1 1 0 1 0 0 1 0 0 0),
(1 1 0 1 0 1 1 1 1 0 1 1 0 1 0 0),
(0 1 0 1 0 1 0 0 1 1 0 0 0 0 1 0),
(0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1),
(1 1 1 1 0 0 1 0 0 1 0 1 0 1 1 1),
(1 0 1 1 0 1 1 0 1 0 1 0 1 0 1 1),
(0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 1),
(0 0 1 0 0 1 1 1 0 0 0 1 0 0 1 0),
(1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0),
(1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0),
(0 1 1 0 0 0 1 1 1 1 1 0 1 1 1 0),
(0 1 0 0 0 1 1 0 0 0 0 0 1 1 0 1),
(1 1 0 0 0 1 0 1 0 1 1 1 1 0 1 1),
(1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1),
(0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1),
(0 0 0 0 1 1 0 0 1 1 0 0 0 1 0 1),
(1 0 0 0 1 1 1 1 1 0 1 1 0 0 1 1),
(1 1 0 0 1 0 1 1 0 1 0 0 1 1 1 1),
(0 1 0 0 1 0 0 0 0 0 1 1 1 0 0 1),
(0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0),
(1 1 1 0 1 1 1 0 1 0 1 0 1 1 0 0),
(1 0 1 0 1 0 1 0 0 1 0 1 0 0 0 0),
(0 0 1 0 1 0 0 1 0 0 1 0 0 1 1 0),
(0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 1),
(1 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1),
(1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1),
(0 1 1 1 1 1 1 1 0 0 0 1 0 1 0 1),
(0 1 0 1 1 0 1 0 1 1 1 1 0 1 1 0),
(1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0),
(1 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0),
(0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 0),
(0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1),
(1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1),
(1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1),
(0 1 0 1 0 1 0 1 1 0 1 0 1 1 1 1),
(0 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0),
(1 1 1 1 0 0 1 1 0 0 1 1 1 0 1 0),
(1 0 1 1 0 1 1 1 1 1 0 0 0 1 1 0),
(0 0 1 1 0 1 0 0 1 0 1 1 0 0 0 0),
(0 0 1 0 0 1 1 0 0 1 1 1 1 1 1 1),
(1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1),
(1 1 1 0 0 0 0 1 1 1 1 1 0 1 0 1),
(0 1 1 0 0 0 1 0 1 0 0 0 0 0 1 1),
(0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 0),
(1 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0),
(1 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0),
(0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0),
(0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0),
(1 0 0 0 1 0 0 0 1 0 1 1 0 1 0 0),
(1 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0),
(0 1 0 0 1 1 1 1 0 0 1 1 1 1 1 0),
(0 1 1 0 1 0 1 0 1 1 0 1 1 1 0 1),
(1 1 1 0 1 0 0 1 1 0 1 0 1 0 1 1),
(1 0 1 0 1 1 0 1 0 1 0 1 0 1 1 1),
(0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1),
(0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0),
(1 0 1 1 1 1 1 1 1 0 0 1 1 0 0 0),
(1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 0),
(0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0),
(0 1 0 1 1 1 0 1 1 1 1 1 0 0 0 1),
(1 1 0 1 1 1 1 0 1 0 0 0 0 1 1 1),
(1 0 0 1 1 0 1 0 0 1 1 1 1 0 1 1),
(0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1),
(0 0 0 1 0 1 1 0 0 1 0 1 0 1 0 0),
(1 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0),
(1 1 0 1 0 0 0 1 1 1 0 1 1 1 1 0),
(0 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0),
(0 1 1 1 0 1 1 1 0 1 0 0 1 0 1 1),
(1 1 1 1 0 1 0 0 0 0 1 1 1 1 0 1),
(1 0 1 1 0 0 0 0 1 1 0 0 0 0 0 1),
(0 0 1 1 0 0 1 1 1 0 1 1 0 1 1 1),
(0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 0),
(1 0 1 0 0 0 1 0 0 0 0 0 1 1 1 0),
(1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 0),
(0 1 1 0 0 1 0 1 1 0 0 0 0 1 0 0),
(0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1),
(1 1 0 0 0 0 1 1 0 0 0 1 0 0 0 1),
(1 0 0 0 0 1 1 1 1 1 1 0 1 1 0 1),
(0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 1),
(0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1),
(1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 1),
(1 1 0 0 1 1 1 0 0 1 1 1 0 1 0 1),
(0 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1),
(0 1 1 0 1 0 0 0 1 1 1 0 0 0 0 0),
(1 1 1 0 1 0 1 1 1 0 0 1 0 1 1 0),
(1 0 1 0 1 1 1 1 0 1 1 0 1 0 1 0),
(0 0 1 0 1 1 0 0 0 0 0 1 1 1 0 0),
(0 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1),
(1 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1),
(1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 1),
(0 1 1 1 1 0 1 0 0 0 1 0 1 1 1 1),
(0 1 0 1 1 1 1 1 1 1 0 0 1 1 0 0),
(1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 0),
(1 0 0 1 1 0 0 0 0 1 0 0 0 1 1 0),
(0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0),
(0 0 0 1 0 1 0 0 0 1 1 0 1 0 0 1),
(1 0 0 1 0 1 1 1 0 0 0 1 1 1 1 1),
(1 1 0 1 0 0 1 1 1 1 1 0 0 0 1 1),
(0 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1),
(0 1 1 1 0 1 0 1 0 1 1 1 0 1 1 0),
(1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0),
(1 0 1 1 0 0 1 0 1 1 1 1 1 1 0 0),
(0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 0),
(0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1),
(1 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1),
(1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1),
(0 1 1 0 0 1 1 1 1 0 1 1 1 0 0 1),
(0 1 0 0 0 0 1 0 0 1 0 1 1 0 1 0),
(1 1 0 0 0 0 0 1 0 0 1 0 1 1 0 0),
(1 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0),
(0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0),
(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
(1 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0),
(1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0),
(0 1 0 0 0 1 0 0 1 1 1 1 1 1 0 0),
(0 1 1 0 0 0 0 1 0 0 0 1 1 1 1 1),
(1 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1),
(1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 1),
(0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 1),
(0 0 1 1 0 1 1 1 0 0 1 0 1 1 0 0),
(1 0 1 1 0 1 0 0 0 1 0 1 1 0 1 0),
(1 1 1 1 0 0 0 0 1 0 1 0 0 1 1 0),
(0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 0),
(0 1 0 1 0 1 1 0 0 0 1 1 0 0 1 1),
(1 1 0 1 0 1 0 1 0 1 0 0 0 1 0 1),
(1 0 0 1 0 0 0 1 1 0 1 1 1 0 0 1),
(0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1),
(0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 0),
(1 0 0 1 1 1 1 0 1 1 1 0 0 0 0 0),
(1 1 0 1 1 0 1 0 0 0 0 1 1 1 0 0),
(0 1 0 1 1 0 0 1 0 1 1 0 1 0 1 0),
(0 1 1 1 1 1 0 0 1 0 0 0 1 0 0 1),
(1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1),
(1 0 1 1 1 0 1 1 0 0 0 0 0 0 1 1),
(0 0 1 1 1 0 0 0 0 1 1 1 0 1 0 1),
(0 0 1 0 1 0 1 0 1 0 1 1 1 0 1 0),
(1 0 1 0 1 0 0 1 1 1 0 0 1 1 0 0),
(1 1 1 0 1 1 0 1 0 0 1 1 0 0 0 0),
(0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0),
(0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 1),
(1 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1),
(1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 1),
(0 0 0 0 1 1 1 1 0 1 0 1 1 0 0 1)
]
*/
return Matrix(N16) ;
end intrinsic ;
</code>
</pre>
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