00:02:23 <int-e> So in the case of BCH codes you'd have an n+2 code over GF(2^k), but I'm trying to think over GF(2) here.

00:02:45 <b_jonas> no idea. hey, I passed an exam about codes but that was under the algebra dept, they teach the hardest stuff in all subjects but don't actually require you to know anything in exams. so I don't know anything about how codes work.

00:15:56 <int-e> shachaf: I think this matrix http://paste.debian.net/1260517/ makes a (3+2)2 code in that sense. Note that 3+2 > 2^2

00:27:35 <shachaf> I guess this sort of flexibility is why you wanted to scrap fields and be linear over GF(2).

00:32:25 <int-e> anyway, this is totally unsystematic... BCH codes are a nice, general construction.

00:35:18 <int-e> shachaf: In the "systematic code" sense, yes. But not in the sense of a construction leading up to the full matrix.

00:35:55 <int-e> And the former is mainly because I started with an identity matrix *without loss of gnerality*, and the same thing for the identity matrix blocks at the top of the 4th and 5th column.

00:37:07 <shachaf> (Multiplying a row by something messes up the identity matrix, but then you can multiply that column by the inverse to unmess it.)

00:38:13 <shachaf> You multiply a row by something and then multiply one of the identity matrix columns by its inverse.

00:39:35 <int-e> It'd require some sort of conjugation-esque trickery. After making the code systematic I only considered multiplications by an invertible matrix from the right.

00:40:25 <shachaf> Hmm, also I'm still thinking of the field case here, and I guess these things aren't a field, so I might be confused.

00:42:44 <int-e> I can multiply each row to get an identity matrix into the corresponding block of the 4-th column. And then I can multiply the first three *columns* to restore the identity matrices there.

00:46:25 <int-e> But if we do the above to make the fourth column all 1s, we get [1,1;0,1]*[1,0;1,1] and its inverse in the last column, which has order 3.

00:48:45 <shachaf> Of course there are 1+p and n+1 codes for any n/p. And there are n+p codes for any n/p where n+p <= 4.

00:51:53 <int-e> And,.. that's actually forced to make a 5th column; there are simply not enough invertible 2x2 matrices.

00:54:35 <int-e> There are still two choices left, so this doesn't contradict your 3+3 code claim... in fact that does work out.

01:03:56 <int-e> Ah, the same thing happens... after all the w.l.o.g. reductions we're forced into GF(4).

01:12:32 <int-e> You can rephrase the criterion for the parity matrix as "every kxk block for k <= p is invertible"

01:13:14 <int-e> (you select columns directly, and rows by picking the remaining rows as columns from the direct-mapping identity matrix part)

01:23:35 <int-e> The horizontal arrows... well, basically you can use column operations to make those row all zero there.

01:25:21 <int-e> I think I actually *learned* this back at university. But I didn't understand why and we never used it and I forgot.

10:35:46 <esolangs> [[Alphaton]] https://esolangs.org/w/index.php?diff=104678&oldid=104675 * ColonelMatthew97 * (+117)

10:36:03 <esolangs> [[Alphaton]] https://esolangs.org/w/index.php?diff=104679&oldid=104678 * ColonelMatthew97 * (+1) /* Updates (v0.7+) */

10:36:42 <esolangs> [[Alphaton]] https://esolangs.org/w/index.php?diff=104680&oldid=104679 * ColonelMatthew97 * (+0)

11:28:17 <esolangs> [[Alphaton]] https://esolangs.org/w/index.php?diff=104681&oldid=104680 * ColonelMatthew97 * (+1) /* Commands */

11:34:18 <esolangs> [[Alphaton]] https://esolangs.org/w/index.php?diff=104682&oldid=104681 * ColonelMatthew97 * (+424)

11:35:08 <esolangs> [[Alphaton]] https://esolangs.org/w/index.php?diff=104683&oldid=104682 * ColonelMatthew97 * (+8)

11:35:41 <esolangs> [[Alphaton]] https://esolangs.org/w/index.php?diff=104684&oldid=104683 * ColonelMatthew97 * (+23) /* v0.8 - 13/Nov/2022 */

11:48:35 <esolangs> [[Alphaton]] https://esolangs.org/w/index.php?diff=104685&oldid=104684 * ColonelMatthew97 * (+49) /* v0.8 - 13/Nov/2022 */

16:53:39 -!- razorlovesbees has set topic: Welcome to the definitive cult of esoteric programming language design, dry-cleaning, and DNA modification! | https://esolangs.org | logs: https://logs.esolangs.org/a.

16:53:45 -!- razorlovesbees has set topic: Welcome to the definitive cult of esoteric programming language design, dry-cleaning, and DNA modification! | https://esolangs.org | logs: https://logs.esolangs.org/.

17:07:50 <int-e> It's okay... the most important part of the topic is the link to the logs because that's mandated by Libera. And you fixed it.

19:37:52 <HackEso> Welcome to the international hub for esoteric programming language design and deployment! For more information, check out our wiki: <https://esolangs.org/>. (For the other kind of esoterica, try #esoteric on EFnet or DALnet.)

19:57:10 <nesuniken[m]> Does anyone know of any languages with reverse lexical scope (i.e if scope A is defined within scope B, B can access variables defined in A, but not the other way around)?

20:52:28 <nesuniken[m]> <b_jonas> "it only happens with unnamed..." <- Perhaps this is just a VC++ issue, but nesting them isn't working like I described

21:07:24 <nesuniken[m]> I was hoping for a reverse lexical scope you could nest repeatedly like you can with the regular kind.