manuscript in progress, 2004.
The links below give the kernel k[1..7] of h1
over Z8
with the restrictions 0 < k[2],k[6] < 4 and 0 < k[4] < 2.
The missing members of the kernel may be obtained by incrementing
k[2] by {4}; k[4] by {2,4,6}; k[6] by {4}.
That is, each line in the file corresponds to 2*4*2 = 16 kernel elements.
A typical line in this table looks like 5 2 3 0 3 1 7,
meaning that the polynomial
(1+z)5(1+2z)2(1+3z)3(1+4z)0(1+5z)3(1+6z)1(1+7z)7
(mod 8) is of the form 1 + O(z2).
The exact value is:
1+z2+7z4+7z6+2z8+2z10+6z12+6z14+5z16+5z18+3z20+3z22.
Links: Z8kerH1rep.txt or zipped
Z8kerH1rep.txt.zip.
The links below give the kernel k[1..7] of h2 over Z8
with the restrictions 0 < k[2],k[6] < 4 and 0 <= k[4] < 2.
The missing members of the kernel may be obtained by incrementing
k[2] by {4,8,12};
k[4] by {2,4,6,8,10,12,14};
k[6] by {4,8,12}.
That is, each of the 4096 = 212 lines in the file
corresponds to 4*8*4 = 128 = 27 kernel elements,
for a total of 219 elements in the kernel.
A typical line in this table looks like 15 4 13 6 5 12 15,
meaning that the polynomial
(1+z)15(1+2z)4(1+3z)13(1+4z)6(1+5z)5(1+6z)12(1+7z)15
(mod 8) is of the form 1 + O(z4).
An expansion up to O(z32) is:
1+4z4+2z8+4z12+7z16+4z24+O(z32).
Links: Z8kerH2rep.txt or zipped
Z8kerH2rep.txt.zip.
The links below give the kernel k[1..7] of h3
over Z8
with the restrictions 0 < k[2],k[6] < 4 and 0 < k[4] < 2.
The missing members of the kernel may be obtained by incrementing
k[2] by {4,8,12,16,20,24,28};
k[4] by {2,4,6,8,10,12,14,16,18,20,22,24,28,30};
k[6] by {4,8,12,16,20,24,28};
That is, each of the 4096 = 212 lines in the file corresponds to
8*16*8 = 210 kernel elements, for a total kernel size of
222.
A typical line in this table looks like 5 2 3 0 3 1 7,
Links:
Z8kerH3rep.txt or zipped
Z8kerH3rep.txt.zip.