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• CG 9:13 pm on April 28, 2010 Permalink | Reply Tags: christof paar ( 2 ), composite field ( 16 ), galois field

Christof Paar, “Efficient VLSI Architectures for Bit-Parallel Computation in Galois Fields”, Dissertation, Institute for Experimental Mathematics, Universität Essen, Germany, 1994.

• CG 1:58 pm on February 2, 2009 Permalink | Reply Tags: galois field, normal basis ( 4 ), polynomial basis ( 4 )

2. For what conditions ONB representation is available?

Answer: One condition is when the $p(x)$ generates GF elements which are linearly independent.

Constructing a field

Have just finished reading Chapter 4 from “Finite Fields for Computer Scientists and Engineers – Robert J. McEliece”.

I’ve been away from the computer and spend the whole morning scribbling some calculation on constructing a field. Me now understand that when we have an Euclidean domain $D=F_{2}\left [x \right ]$ with for example $p\left (x \right )=x^{4}+x+1$, that $p$ is irreducible because $p\left (0 \right )=1$ and $p\left (1 \right )=1$, so $p\left (x \right )$ has no zeroes in $F_{2}$.

bla bla bla bla … i have many pages of scribbles…

But I’d like to post this tables here just for a quick reminder for me, it’s unfinished but I’ve got the idea so keeping it up here will be useful someday when I forgot about this $F_{2}^{m}$ stuff 😀

wow! CG with paper and pen! 😀
sudah lama tidak begini.
kalau tidak salah, terakhir waktu mac-nya rusak ya? hahaha.

boleh minta dijelasin lagi tentang ini?

biasanya kalo lagi ada ide, CG suka kerja sambil ngejelasin.

• Budi Rahardjo 11:11 pm on January 29, 2009 Permalink | Reply

jadi F 2 pangkat 3 beda dengan F 8 ya? masih belum mengerti bedanya (terutama di bagian sebelah kanan mod itu).
terus, yang F 2 pangkat 3 itu ada inversenya?

$F_{2^{3}}$ sama dengan $F_{8}$ hanya kalau $F_{8}$ elementnya 0, 1, … 7.

$F_{2^{3}}$ ada inverse-nya.

Math Polynomial

Move forward to Galois Field representation in C. Zooming in all the modules of math for polynomial representation with the prime number 2 as the modulus (means that the coefficient and only take values of 0 or 1).

The text converting code is halfway to go.

Aaaaaa…. selalu pengen belajar Galois, waktu itu pernah mau belajar tentang Galois waktu sedang seneng baca tentang ehmm…mmm… kayanya tentang social network dan transformasi-transformasi gitu… aaaaaa… cerita-cerita

yuti: hah, gue sampe skarang juga belum ngerti2x yut 😀

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