Timeline for Exponential sums over finite fields with even characteristic
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 14, 2011 at 7:09 | comment | added | Jyrki Lahtonen | The technique generalizes to linearized polynomials, i.e. polynomials where only terms of degrees that are power of the characteristic occur. This technique is relatively common in finite fields, and coding theorists often use this trick, when studying quadratic forms in char 2. The classic tome Finite Fields by Lidl & Niederreiter (Cambridge Univ. Press) is the reference. | |
| Sep 14, 2011 at 4:37 | comment | added | Noam D. Elkies | @David: you're welcome & thanks & that was quick :-) | |
| Sep 14, 2011 at 4:36 | vote | accept | David | ||
| Sep 14, 2011 at 4:35 | answer | added | Noam D. Elkies | timeline score: 20 | |
| Sep 14, 2011 at 4:20 | comment | added | David | @Noam. Thank you for your insight. If you add your comment as an answer, I would love to accept it. | |
| Sep 14, 2011 at 3:57 | comment | added | Noam D. Elkies | Trace is additive, and ${\rm Tr}(u) = {\rm Tr}(u^2)$ for all $u$, so $ax^2+bx$ has the same trace as $(a+b^2)x^2$. Therefore the sum is $2^r$ if $a=b^2$ and zero otherwise. | |
| Sep 14, 2011 at 3:49 | comment | added | David | It should also be noted that the method for evaluating such sums over finite fields of odd characteristic is to complete the square, which is not applicable in the above case. | |
| Sep 14, 2011 at 3:04 | history | asked | David | CC BY-SA 3.0 |