## Tagged: galois field Toggle Comment Threads | Keyboard Shortcuts

• #### 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 😀

• #### soni 6:46 pm on January 29, 2009 Permalink | Reply

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?

• #### CG 9:15 am on January 30, 2009 Permalink | Reply

$F_{2^{3}}$ 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.

• #### yuti 9:53 pm on January 1, 2009 Permalink | Reply

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

• #### CG 4:44 am on January 2, 2009 Permalink | Reply

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

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