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September 16th, 2016, 03:06 AM   #1
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Permutation Polynomials

My question is based on permutation polynomials.

A polynomial is said to be a 'Permutation Polynomial' of a finite field if it induces a one-to-one map from the field to itself.
After searching for methods ,still I am unable to form a proper polynomial as shown in examples from specific paper.

I have a doc file which explains the whole construct but the size limit wont let me post it. Is there any way I can post my question?

Regards
classkid
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September 16th, 2016, 03:11 PM   #2
SDK
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Quote:
Originally Posted by classkid View Post
My question is based on permutation polynomials.

A polynomial is said to be a 'Permutation Polynomial' of a finite field if it induces a one-to-one map from the field to itself.
After searching for methods ,still I am unable to form a proper polynomial as shown in examples from specific paper.

I have a doc file which explains the whole construct but the size limit wont let me post it. Is there any way I can post my question?

Regards
classkid
Doesn't $x^p-1$ work for any field of characteristic $p$? For any $x < p$, $x^{p-1}$ modulo $p$ is 1 so evaluation for each such $x$ results in the values $\{x - 1 \ : x \in \mathbb{Z}_p\}$ which is just a permutation on $\mathbb{Z}_p$.
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