Timeline for Some sums related to a quadratic polynomial over $\mathbb{F}_2^n$
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| May 13, 2019 at 13:37 | comment | added | Will Sawin | @shurtados It seems that the squaring and change of variables method can be used to give a lower bound on the original sum $| \sum_k a_k(c) |$, at least when (in the odd case) the sum of $c_i$ vanishes mod two or (in the even case) the sums of $c_i$ over both odd and even $i$ vanish. In this case, one of the $a_k$ must be large. If one of the $a_k$ is large for $c$, the same is true after adding the all-ones vector. This handles the entire odd case and half the even case. | |
| May 13, 2019 at 6:19 | comment | added | shurtados | I'll modify the question to make that more clear. | |
| May 13, 2019 at 6:18 | comment | added | shurtados | Dear Will, thanks for your answer. This only shows that there exists $c$ for which the statement doesn't hold, and not that is not true for any $c$ as I think it might be true. Do you see a way of proving the same for any $c$? | |
| May 13, 2019 at 4:00 | history | answered | Will Sawin | CC BY-SA 4.0 |