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02:05:25 <shachaf> Here's a sort of surprising thing: I generated GF(256) N+P codes using three methods -- Vandermonde, Cauchy, and Lagrange -- and normalized them to be systematic and to have each row and column of the non-systematic part start with 1s.
02:05:32 <shachaf> And they all generate the exact same codes! How come?
02:14:56 <b_jonas> maybe there was only one code wearing different costumes?
02:18:08 <int-e> What's the Cauchy way?
02:18:52 <int-e> The Vandermonde and Lagrange way are the same if you map the field elements to the same columns.
02:19:37 <int-e> since the "normalization" step transforms the Vandermonde matrix such that the first n points are interpolated by a polynomial instead.
02:19:52 <int-e> which is what Lagrange does as well.
02:20:17 <int-e> if you permute the field elements, things should be more interesting
02:20:55 <int-e> > let f n = product [2^n - 2^k | k <- [0..n-1]] in map f [1..4]
02:21:28 <int-e> > let f n = product [2^n - 2^k | k <- [0..n-1]] in map f [5..]
02:21:29 <lambdabot> [9999360,20158709760,163849992929280,5348063769211699200,6996123100331976425...
02:23:04 <int-e> shachaf: If you make a Vandermonde matrix out of the 127 non-zero elements of GF(2^7), is there a square minor with zero determinant?
02:24:12 <int-e> (the 2x2 minors are fine)
02:25:39 <Sgeo> Is Prismata dead?
02:27:23 <Sgeo> Digital card game shachaf has repeatedly tried to get a match with me against, after I lost repeatedly.
02:28:08 <int-e> Yeah I found it. Letting a web site certificate expire isn't a good time... espcially when that happened 15 months ago.
02:29:19 <int-e> (Sorry, I have a habit of expressing my ignorance while simultaneously engaging a search engine.)
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02:30:00 <int-e> (Which is probably annoying, but I can't promise that that's enough to shake it.)
02:41:57 <int-e> https://steamcommunity.com/app/490220?snr=1_2108_9__2107#scrollTop=3840 indicates that this is /may/ be a bit of a Corona victim; they were preparing for GDC 2020 and that got cancelled. And they don't have much of an income stream.
02:43:21 <int-e> doesn't look great :P
03:06:10 <esolangs> [[THROBOL]] https://esolangs.org/w/index.php?diff=104686&oldid=104366 * BoundedBeans * (+429) Added Additional command guidelines section
03:36:42 <shachaf> int-e: The Cauchy way just makes m[row][col] = 1/(row^col)
03:36:53 <shachaf> (For col in [0,N), row in [N, N+P).)
03:37:54 <shachaf> int-e: I think the answer is no even with all 128 elements.
03:38:59 <int-e> shachaf: with 128 elements you get minors of the form [0,alpha^1;0,alpha^2]
03:39:35 <int-e> actually why didn't I take alpha=1... [0,1;0,1]
03:40:07 <shachaf> That's a good point. But I think this matrix does give you a valid code.
03:41:35 <int-e> Yeah but that wasn't where the question is going. Is it still a valid code if you prepend the identity matrix?
03:48:40 <int-e> shachaf: what happens for row in [0,N)? is it the identity matrix there?
03:54:55 <shachaf> Oh, adding an identity matrix to a Vandermonde matrix can certainly produce an invalid code.
03:55:38 <int-e> sure, it definitely wouldn't work for GF(16) or GF(256)
03:55:53 <int-e> But 127 is prime, so it's less obvious.
03:56:54 <int-e> I /expect/ it to still not work. But it'll require a 3x3 minor or larger.
03:57:15 <int-e> Anyway, I don't understand why the Cauchy thing gives you the same code.
03:57:40 <int-e> Nor why there's an inverse in there.
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04:06:19 <shachaf> https://www.corsix.org/content/reed-solomon-for-software-raid discusses these constructions a bit.
04:07:11 <int-e> does it prove that the Cauchy thing works?
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04:11:52 <shachaf> It links to https://proofwiki.org/wiki/Vandermonde_Matrix_Identity_for_Cauchy_Matrix
04:12:04 <int-e> Oh I'm just stupid here actually.
04:13:50 <int-e> We start with the Vandermonde matrix 1/(row^col), and then we use *column* operations to make an identity matrix out of the leftmost n columns.
04:15:14 <shachaf> Hmm, which operations are you allowed to do here?
04:15:15 <int-e> Actually, no, column operations can destroy a code.
04:15:36 <int-e> Row operations can't.
04:15:41 <shachaf> Also you have your rows and columns backwards from the way I've been writing things so it's all very confusing.
04:15:49 <shachaf> (I have N+P rows and N columns.)
04:16:17 <int-e> Oh right. Well, the confusion is mutual.
04:17:00 <int-e> Okay this is completely different from what I thought.
04:17:01 <shachaf> Yes. Sorry, maybe that was unclear.
04:17:17 <shachaf> I'm not sure what ^ would be in a field here. I guess col could be seen as an integer.
04:17:50 <shachaf> Apologies for the confusion.
04:17:57 <shachaf> This is https://en.wikipedia.org/wiki/Cauchy_matrix
04:18:11 <int-e> shachaf: well you *also* identified natural numbers and field elements
04:19:01 <shachaf> I guess I thought ^ would clear it up but it made it worse.
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04:20:58 <int-e> So I guess that page shows that you get the Cauchy matrix from V_y with *row* operations and the one valid column operation, which is multiplying a column by a constant.
04:21:24 <int-e> and again, for you that will be *column* and row.
04:21:50 <int-e> shachaf: I prefer my matrices to be wider than high.
04:21:57 <shachaf> The one valid column operation here is scaling by a constant?
04:22:13 <int-e> shachaf: well, in the sense that it can't destroy the code
04:22:18 <shachaf> You literally said that right after the comma.
04:22:25 <int-e> since it doesn't mix any code data.
04:22:59 <int-e> so you can reverse it even after erasure happened.
04:24:07 <shachaf> Right. I just typed that before reading the rest of your sentence.
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04:26:14 <int-e> Okay, and we can also compute -PV_x^{-1}V_x = -P and multiply by P^-1 from the right to get the identity matrix part.
04:27:28 <int-e> So we do have a transformation of V_x | V_y. And finally, V_y doesn't have to be square.
04:27:57 <shachaf> The program I'm experimenting with these things with is at /tmp/rs.c if that's helpful.
04:28:39 <HackEso> ls: cannot access '/tmp/rs.c': No such file or directory
04:28:55 <shachaf> On my website, which I'm not quoting as a full URL because I don't want Google to start crawling it.
04:31:28 <int-e> So... there's still a puzzle here though. Why does multiplying a shachaf-row by a constant nmot change the code? Or is that something that gets normalized away... ah. It does.
04:32:29 <int-e> Since that's how you make your rows start with 1.
04:41:36 <shachaf> Multiplying a shachaf-row by a constant is fine because you can just divide by the same constant when you get the code, right?
04:41:55 <int-e> Yes but the code words are different
04:43:19 <shachaf> I mean when you get a code word. But maybe I misunderstood.
04:44:27 <int-e> You get /a/ working code but it's a different one unless you multiply and divide by 1.
04:45:02 <int-e> While shachaf-column operations don't affect the set of code words at all.
04:46:58 <int-e> But you did lay out your normalization procedure earlier and it does scale shachaf-rows. So yeah, after doing that, the Cauchy construction will end up the same as the other two.
04:48:20 <zzo38> You mentioned a card game, but can we make up our own card game, involving some of the things involved in esolangs too?
04:48:36 <shachaf> I'm still not sure why the Vandermonde and Lagrange constructions end up giving the same thing.
04:53:37 <int-e> The inverse of the top square of the Vandermonde matrix does polynomial interpolation.
04:53:45 <int-e> Lagrange does polynomial interpolation.
04:54:03 <shachaf> Why does the inverse do polynomial interpolation?
04:54:05 <int-e> It's quite literally the same thing as taking the Vandermonde matrix and turning it into a systematic code.
04:54:43 <int-e> Because polynomial interpolation for fixed coordinates x_1...x_n is the inverse of polynomial evaluation at those points.
04:55:03 <int-e> And Vandermonde matrices do polynomial evaluation.
04:55:34 <shachaf> Right, now that you put it that way it makes sense!
04:55:43 <esolangs> [[Text Binary]] N https://esolangs.org/w/index.php?oldid=104687 * Star651 * (+1739) Created page with "Text binary is a programming language first created by [[User:Star651]] in early 2006 but never written about until November 13, 2022. The concept of text binary is very simple; Text Binary is simply a binary file that has been converted into the textual representat
05:01:49 <int-e> Okay. I think I kind of get the Cauchy matrix thing... let's see whether I get the proofwiki proof as well now.
05:07:06 <int-e> Yeah... it works out. I /think/ doing it just for a single column of C makes it a tiny bit easier, though then you need notation for the non-square Vandermonde matrix that replaces V_y.
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05:18:14 <int-e> Hmm. I'm getting the feeling that working over Galois fields is optimal for this kind of thing (i.e. I'm not seeing any benefit from using arbitrary kxk matrices rather than working in GF(2^k). But I can only try very small k, up to about 4.
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07:23:05 <shachaf> int-e: https://web.eecs.utk.edu/~jplank/plank/papers/CS-05-569.pdf may be relevant.
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09:30:46 -!- b_jonas has set topic: Welcome to the international hub of esoteric programming language creation, condemnation, and coding theory! | https://esolangs.org | logs: https://logs.esolangs.org/.
09:35:04 <b_jonas> I just realized something. freenode/#esoteric was called an international hub way before github was cool. The first mention seems to be by GregorR: https://logs.esolangs.org/freenode-esoteric/2005-10.html#lfU
09:37:12 <b_jonas> we should have trademarked "hub", we'd be rich by now
09:37:41 <b_jonas> that, or we'd have changed history and github would have chosen a different name
09:39:24 <b_jonas> we should have trademarked hub in some small European country where they don't look before choosing the name
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11:29:44 <wib_jonas> I wonder if we could do something alliterating like "esoteric coding center and error-correcting code"
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11:31:21 <Laclale> Unable to log-in from other device
11:33:02 <wib_jonas> Laclale: what error do you get, and also read https://libera.chat/guides/sasl#sasl-access-only-ip-ranges or other https://libera.chat/guides/faq
11:33:48 <Laclale> Forgot password for esolangs wiki
11:34:43 <wib_jonas> Laclale: well then just register a new account with a new password, unless you had privilages on the old account
11:35:10 <Laclale> > You must log in again to verify that you are Laclale.
11:35:12 <lambdabot> <hint>:1:14: error: parse error on input ‘in’
11:35:23 <wib_jonas> though you may try https://esolangs.org/wiki/Special:PasswordReset first
11:35:45 <Laclale> Tried to add e-mail but not working
11:35:54 <wib_jonas> for what user account? also make sure your http client accepts cookies
11:36:26 <Laclale> for Laclale in esolangs wiki
11:37:19 <wib_jonas> then no you don't, so if the password reset doesn't work then create a new account
11:37:40 <Laclale> Can you rename current account
11:45:05 <fizzie> There were some problems in the past with wiki emails, but hopefully not at the moment. So if you still have access to the original account, setting & confirming an email address on https://esolangs.org/wiki/Special:Preferences and then going through https://esolangs.org/wiki/Special:PasswordReset *should* work, in theory.
11:46:48 <Laclale> Can you add email remotely or change name?
11:49:42 <wib_jonas> wait, mediawiki allows you to change your email and then request a password change without knowing your password?
11:50:16 <fizzie> Maybe it doesn't, based on the answer above.
11:50:52 <fizzie> Can you edit pages with your account? If you email me some kind of a token (just some random string) and then after that update your user page to contain that same token, I can probably figure out a way to send you a password reset email.
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11:52:51 <esolangs> [[User:Laclale]] https://esolangs.org/w/index.php?diff=104688&oldid=92820 * Laclale * (+17)
11:53:54 <fizzie> In retrospect I guess you could've just used https://esolangs.org/wiki/Special:EmailUser/Fizzie to tell me where you want your new password to be sent, because it puts the logged-in user's name in the message.
11:54:23 <esolangs> [[User:Laclale]] https://esolangs.org/w/index.php?diff=104689&oldid=104688 * Laclale * (+22)
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12:11:17 <wib_jonas> Lacale: if you still have a login cookie then just download your watchlist https://esolangs.org/wiki/Special:EditWatchlist/raw which is probably the only non-public information you have on the current account, then create a new account and load the old watchlist (plus watch your new user page) and then just use the new account instead of the old
12:22:24 <fizzie> I made an executive decision to manually reset their password given proof of being currently logged in (by editing as the account).
12:22:32 <fizzie> I guess it's technically possible that was a case of cookie theft + social engineering to be able to lock the original user out of their account, I just feel like doing that for an esolangs.org wiki account sounds not terribly likely.
12:32:07 <wib_jonas> doesn't need cookie theft, only social engineering to make them edit a token into their user page without context to prove something else than what you think it proves
12:32:25 <wib_jonas> I mean to make the original owner of the wiki user to do that
12:37:30 <wib_jonas> that is, an active MITM both ways social engineering attack
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13:09:01 <esolangs> [[CTFuck]] https://esolangs.org/w/index.php?diff=104690&oldid=104656 * Pro465 * (+63) /* See also */
13:11:45 <esolangs> [[CTFuck]] https://esolangs.org/w/index.php?diff=104691&oldid=104690 * Pro465 * (+75) /* Turing Completeness */
13:12:13 <esolangs> [[CTFuck]] https://esolangs.org/w/index.php?diff=104692&oldid=104691 * Pro465 * (-63) /* See also */
13:37:54 <esolangs> [[CTFuck]] https://esolangs.org/w/index.php?diff=104693&oldid=104692 * Pro465 * (+0) /* Turing Completeness */
13:42:32 <esolangs> [[THROBOL]] https://esolangs.org/w/index.php?diff=104694&oldid=104686 * BoundedBeans * (+296) Clarified Additional command guidelines
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14:10:40 <esolangs> [[Rockstar]] https://esolangs.org/w/index.php?diff=104695&oldid=101243 * Laclale * (+126) /* Media Coverage */
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23:14:07 <esolangs> [[Bundle]] https://esolangs.org/w/index.php?diff=104696&oldid=99697 * OllyTheFoldy * (+12770) page resurrected