Zsh (+coreutils), 319 bytes

Uses z85 encoding. Attempt this online!

basenc -d --z85<<<'0&M8}p.B@#L#QZE00001Fb*2U02+?qq#={[000069asT6g8.)4ZwEwH000Mg1onA4aoh}/0Q{6?7?7Abap8T<N!#M/0000:ZZ{J%0d$no1{.{L01Y
zs5hjUju{Cb/00eC!f:[8q1oX#k5eUKnfBigKaB[#)FcD1?fA=JG2NyzwD&LsiWGLW<&LA29Gr+T=<o=q3huiZS05#83BRN)l3zmwk01TOWF4#ep&0YP[gY.1d24nhWll]9L
mgYDLaoqEc0f^Fe]ZR$Y'|basenc --base2msbf -w23|sed '$ d'

Encoding steps
. Convert Arecibo message to a digestible format → bitstr.8
. Convert bitstr.8 into binary, using script demo16.sh** → bits.16.again
. Convert binary to z85 → basenc --z85 bits.16.again >bits.85
. Use the z85-encoded string in bits.85 for a much shorter code golf!

Decoding steps -- i.e. what the main script does
. basenc -d --z85<<< decodes the z85 string to binary
. |basenc --base2msbf -w0 decodes binary to Ascii 1s and 0s
. |cut -c-1679 trims extra data

My original solution was 577 bytes, using a custom encoding logic.

Brainfuck, 2360 2008 1938 1902 bytes

-[>+<-----]>---......+.-.+.-.+.-.+.-............>++[-<+.-.+.-.....>]<..+.-.>++[-<.+.-...+.-..>]<+.-.+..-..>+++[-<+.-.+.-.+.-.>]<.+.-..+.-.>+++[-<............>]<+..-..................>++[-<.+..-.+.-..................>]<+.-.+.-.+.-..................+.....-..>+++[-<..........>]<+..-....+...-...+..-....+..-...+.-.............+..-..+.-....+..-.+.-...+..-...+..-....+..-.+.-.>++[-<+.....-.+.....-.>]++[-<............>]<.+.-......>++[-<...........+.-.................>]<+......-.............+.....-.>++[-<...........>]<+..-....+..-....+...-...+..-...>++[-<+.-.......>]<..>++[-<+.-....+..-.>]<..+...-..+..-.+.-.>++[-<+.....-.+.....-.>]++[-<............>]<.+.-......+..-.........+.-...........+..-...............+.-.....+..-..........+......-.....+..-......+.....-..........+..-..........>+++[-<...+.-.....>]<+.-......+..>++[-<-.......+.>]<.-....+..-......+.-..........+..-...+.-....+..-...............+..-..+..-.............+..-...+.-....+..-.........+..-....+..-..>++[-<....+.-...>]++[-<...+.-.....>]<+.-.......>++[-<+..-........+.-...+.-........>]<.+.-.......+.-.....>++++[-<+.-.......>]++[-<.....+..-....>]<....+..-.........+.-...+...-.+.-.+..-...........>++[-<+.-.......>]<.......+.-.....+.....-............+.-....+.-.+...-.+.-..+.-.+..-.+..-......+.-..+...-..+.-..+.......-.+...-....+...-.....+..-.+...-.........+.-.+.-.....+...-.+..-..+.-......+.-.+.-.....+......-..+.-......+.-.+.-.....+..-......+.-.....+..-.+..-..>+++[-<...........>]<+...-.....+.-..............+...-.+.-.+.-...>++[-<+.-.+.-.+.-.>]<.+...-.........+.-.+.-.+.-.+.-................+.-.+.-..............+.....-................+.........-..........>++[-<..+...-.....>]++[-<....+..-.......>]<+..-.+.-.........+.-.+..-..>++[-<...+..-..+..-....>]<+.-.>++[-<..+.-.+.-...>]<+.-....>+++[-<+.-...+.-..>]<......>++[-<+.-...+.-.>]<...........+.-....+.-.>++[-<...+.-.........>]<+.-..............+.-..+.-.+.-...........+....-..+.....-.+.-..+....-...

Try it online!

My idea was to first generate a simple solution consisting of setting up an ASCII 0 followed only by +-. instructions to produce the output. Repeating sections can then be shortened using loops.

Choosing the optimal set of non-overlapping sections for looping basically comes down to solving a maximum-weight independent set problem. Currently, I just use a greedy algorithm which takes the section that can be optimized the most and then removes all conflicting sections. This is then repeated until no sections are left.

Using a more sophisticated algorithm one can surely achieve better results.

Python 3, 331 bytes

exit(''.join(bin(i)[3:]for i in b'`UP@JB`IDQKJjjd`@@@@@L@@Ah@@CP@@J`@@_@@@@@LNLLP@FPtXpu}}}|@@@@`@@`@@@A@@A~@@~@@@CCCcDA@DMCGM____@@@@HF@H@L@@PX@_`pO`A`@HA@HHF@`LLB@FHX@@s@@Xa`CC@`HD@``L@b@XAD@PDDA@PD@C@F@X@ck@A@P@BCx@DKi[@gI\x7f\\NC\\@TGY@hOrAPXDFp@@@@@\\D@@zbjipAU@@B`@Gp@@\x7fx@G@\\@X@LAh@lFXCLHhJHQHdPBJH@DHP@H@`@Dh@OOix')[1:])

Try it online!

05AB1E, 182 bytes

•sv¯ö¨₁ÿ.ÛïžôΔ¨γ_Ígv…=Bм„Ð.(ܦi´…ε±G½0^/₃öRÛž¼¤"āêL!ˆ6‘Gā܇ðв₁÷Ã7€₂䬂Cć¨g¾†@÷[_-68¯a∍iG*6ÆîÆ;>éjζãÎÂ+ºžnî¼ć'(ÝÞΔ‹∞ÉݹÕ5λ₆*a|§oÄmôæ¨;—:hž¥ð¢ocË'¨%¡4Ćáß©ìća;FÁ?iˆèεƒʒ•Ž6–FD4‰`3ÊD?i-

Try it online! (uses 1 for 0 and 0 for 1, as allowed by the question).

Try it online! (5 bytes longer, 0 for 0 and 1 for 1, added newlines for readability).

Most of the code is a base-255 integer constant N, the rest is an Asymmetric Numeral System decoder, using hardcoded probabilities of 75% / 25% (the actual frequency of 0 is 76.35%, which is so close to 75% that it would only save 1.2 bits in the payload, while the nice and round 75% lets us save several bytes in the decoder).

Ž6–F                  # repeat the following 1679 times:
    D                 #  duplicate N
     4‰`              #  divmod 4: pushes N / 4, N % 4 on the stack
        3Ê            #  is N % 4 != 3 ? (boolean 1 or 0)
          D?          #  print a copy
            i-        #  if it's 1, subtract: N = N - (N / 4)
                      #  (otherwise, N = N / 4, since that's the top of the stack)

Here's the ANS encoder that generated the constant: Try it online!

Î                          # start from N = 0
 Rv         ]              # for each bit in the reversed input:
   4*                      #  N *= 4
     yi                    #  if the bit is 1:
       3+                  #   N += 3
         ë                 #  else:
          3÷               #   N /= 3 (integer division)
             ₅B'•.ø        # compress N as base-255

C++ (gcc), 748 bytes

#define l(X,Y)if(z[i]==#X[0])z.replace(i,1,#Y);
void f(){std::string z = {"ab1eeedala1ebeeheal1mmma1fa1g1eeeeeeea1a1alddhgdbcdgdacedgdacedgdeeedgdndgddhgqiafbcag1dbfa1blceafafbcegcinnnlddhgmddegddhgb1ddelcidbnlddhgqqiafag1hedeblcebcaf1acegcinnnlddhgmhcdegdacdagb1bfda1lcibfhcildacdaga1d1d1almhcheagbqch1blhcmbqgdacachghcmbqgbqch1blmh1d1aga1hfd1aledcd1aledeheaga1heheblmdbqgbcdchga1af1efdga1hedbla1bndala1b1f1ea1fflh1aia1acccl1f1bibff1ldeebf1fla1h1ebfccla1h1ebfbla1bffdalddhgaibedblaieemeeeeelaideeeealdh1ehldcidalhcccidlbihf1hlafdafbgacedefblfachfacagemebeemagema1ma1magbememhgbeb1b1hgbedehghea1edalfcacieacca0"};for(int i=0;i<1751;i++){l(q,cb)l(n,fi)l(m,ae)l(i,c1)l(h,ba)l(g,0l)l(f,0c)l(e,01)l(d,bb)l(c,11)l(b,aa)l(a,00)l(l,\n)printf("%c",z[i]);}}

Try it online!

By replacing the most used substring with a new character until it's not worth it anymore

Perl 6, 276 bytes

:122[q{3tD!gLF['u#.K>'uCG8cvJZ[on1Z<D!	`Fhqq-_V'"qQn+n0h\:b,vXjo&1
TMFaW;wvX;eUS
(ueelNSu,y93\kjGI&?UU/38 :ndi4Y5cyC+ME\g7LWaS;QLjtD^L+aVd(XW%gy\8'Eqk-+f72S5J?(r5!m^5px T[Z'3&jd0lZ'/
x%#(}.ords].base(2)~~S/.//.say

Try it online!

Outputs as a series of 1679 0s and 1s. You can have it on different lines by adding .comb(23)>> before the say.

Explanation:

:122["...".ords]                     # Convert the string from base 122
                .base(2)             # To base 2
                        ~~S/.//      # Remove the leading 1
                               .say  # And print

I can probably save bytes by using the output as a 1679 bit integer instead, or reversing the bit representation.

C++ (with Gnu multi-precision library), 359 bytes

This outputs the string as one line. It uses '1' for 0, and '0' for 1 :/

It simply reads the embedded string as base 62, and prints it as base 2.

Use g++ -g arecibo.cpp -lgmp -lgmpxx to compile and link

#include<gmpxx.h>
main(){mpz_out_str(stdout,2,class_mpz("vuXXKBYAu1hPsJPbFSf49akyFd0bjJbMIV3upYndU8kYFPsXcpRUK6c9qnzLfORxkxGL7ZfoSwgSxFbCrydjHL603QcxexopAzoYAcAyEiENJJU2vQA2zM8NDbeY6nHgL8rfFoPJaclwxx6TeKeOEknEQHzp7C4la3o8xijBQLOVweFZ1CI9dXy2VQhgnuwF5FeW5mQ909pRMxhn6G3RJ1QEtkS7oGMZYHM03fh4fj391IoYLGVv3iUVuTrV2ghz9CUa9hfGYrdhGoVE2w1inYalYl",62).get_mpz_t());}

Tcl, 366 bytes

binary scan [binary decode base64 QBUACgpIRKSpqkoCAAAAgAEAsAAAWAAAKgAAHwAAAGA4hhEATFiMYX3f9wEAAAgAIAAAAAQA8AOADwAAGIZjBAQQFsZZ3/d9AAAAAgMIgAEAwQD8YOADMAAIECAIDAgYBgIwwgCAGQCMMIBhICAQIAgYIAIMEAEEBAEBAQFgAAMMIK4BEBAACD4AhC5tICd/h4MdQMFNoOAnUDAQbAAAAAAcBACuqCoHUAUAKADwAQD+A8ABBzAABiyABjNghigoQiQSAaIIACEEgAACACkAni8P] b* z
puts [join [regexp -all -inline .{23} $z] \n]

Try it online!

Piet, 1763 codels

Outputs a stream of 0s and 1s (no line breaks).

Codel size 1:

Codel size 4, for easier viewing:

Explanation

• First, push a sentinel value of -1 onto the stack.
• Then push the Arecibo message, in reverse order (because it's a stack), using run-length encoding.
• Finally, alternate between two loops, one printing zeroes and the other printing ones.
  • The loop counter is the current stack value, decremented until it hits zero, at which point it is discarded and we switch to the other loop.
  • Between the zeroes-loop and the ones-loop, check for the sentinel value, exiting if it is found.

Notes

The program follows a spiral path, clockwise from top left into the centre. The scattered black blocks that roughly follow the diagonals are the flow control. Here's the trace from NPiet.

I've been working on this since the day this challenge went up, but it took a little bit of time to get the message "written" into the picture! I wrote the final loops and the sentinel value first, and then built up the message from the centre outwards. (Since Piet always starts execution from the top left, I expected to have to shuffle and rotate the image around to avoid excess whitespace, but it fit perfectly!)

Fun fact: Run-length encoding in Piet doesn't (by itself) save any space. It takes n codels of one colour to push the value n onto the stack, or n codels of different colours to push that many 1s onto the stack. So it's the same number of codels either way. But the bigger numbers that RLE gives you mean you can use arithmetic tricks (e.g. instead of pushing 9, you can push 3, duplicate, and multiply) to reduce the number of codels, and funny-shaped blocks to fill in available whitespace.

I wasn't sure about how to count score for Piet entries. I found some that seem to count all codels, and others that explicitly only count those actively used. I just counted them all; ignoring white codels (even those that the program never moves through) seems akin to ignoring whitespace in a more typical programming language.

Oh, and I've just now (two hours after posting) realised that I wasted the last bit of time working on this. I wanted to trim off the almost-completely-white last row and column, so I shuffled things around... including the black flow-control blocks. But the edges of the image work the same as black! If I'd just remembered that, I wouldn't have needed to spend so much time puzzling over the intricacies of DPs and CCs...

Java, 688 678 590 379 361 bytes

Returns a string.

n->new java.math.BigInteger("in95mzupnpa2r0khpoepyql6ioqyn413avucdtfay6indx4wh9dehe3sn18klobtf4z9g9q17umqmwpegr2khb5eqinn7azl4jpfp2a8eui0xfrx5qwrou6gd65jh4ge3ls14k5lu7qrvmg6942ms29u5rb8fa6yrdhfoh5zoi9bdi7uh5ig0u0ff9kounth8sh357x7qox4m3oqviqsbrvakonbka4ahp21bgzi5v1akzzuqoncszhpabbru9q1uo2g11zr73iuyiqr5ikr69zn7cdv7e1lhd6ese9",36).toString(3).replace("2","0000")

-10 bytes by returning the raw stream (old answer)
-88 bytes by using base 10 numerics (thanks @ceilingcat!)
-211 bytes (I knew it could be golfed!) by using a base-36 encoded BigInteger (thanks @JollyJoker!)
-18 bytes by using a different encoded integer (thanks again @JollyJoker)

Try it online!

Explanation:

n->new java.math.BigInteger("base36 string",36) // Decode the base-36 integer.
   .toString(3)                                 // Re-encode as ternary
   .replace("2","0000")                         // Replace 2 with "0000"
                                                // Implicit return

MathGolf, 223 220 bytes

'06*"x·<×J× Ç×►B×ê\"@$↕!◙è0♥f░×→0×♠p└☺α?×└•×◙×P♣p¬è:×►∟××××←♦♠♣≥â☻┘A☺▄αp⌂r☻[║►×>◘×♦♦└:☻↑`×♥@@@@►►@♦↑ ☻♀◘☻♦☻☻├×å↑×╠×Ç!♠ 0♀◘↑◘☻♦◘×♠α♥â▼ÇA×└×◘` ×××▀≈}═14♦►►π0♀××°×α•×►×××☻×◘××└≈}_├↑♪↓×─0♫♥×××|××*××♪×Ç♠×└×××× ⌐¬╩↕◄○((×T☺"$à+

Try it online!

Explanation

'0                push single character "0"
  6*              repeat 6 times
    "..."         push the magic string
         $        convert to ordinal
          à       convert to binary string
           +      pop a, b : push(a+b) (add the 6 zeroes)
                  below is the footer
            L/    divide into groups of 23 characters
              n   join array with newlines into string

[Python 2], 345 bytes

s=''
for c in")pG/K(K*j$h%kk$ppjGE&I6S6S5[5eCv~vw0x&z$wgqcde$e=G4G?G4eG0e:vv~w*G,gn$wy$uuuuG=G)I,G.I2G(I-eG(I)e-I0G+G+G(G)I*G*vI)G-w'I2y0w'I,vI)G*G)G+G(G*I+W+I+W,G*G(G*G*G*G/I,I+I,iq.G*G1G(e/g$c%sG)m%md~$M(},K(cO)K(eO)K(I)G(aE$M(G1c$hpoI,pG3K1e3eU/M*M,I.I*S,Q(y*y'hG(ng&j$j$G+hW/g'G/G,G1k.d$e$mN":c=ord(c)-35;s+=[bin(c-35)[2:],'0'*c][c<35]
print s

I encoded the length of strings of 0s as a byte starting at chr(31). Then I encoded the remaining 10101 as binary numbers starting at chr(70) up to chr(126). Binary strings that didn't fit were split up into smaller chunks.

Edit: Reduced to 326 bytes. Thanks Jo King

Edit: Fixed a bug in the code generator program

Edit: Final Edit

Perl 6, 348 bytes

{"000000"~:36<5r0afnfm8wyke8tfy1pwt7xnuaxyh3wodfp7bhsdufyw0xbdp1pumrz2xir652tuc0ss9oec8yad9vefivd66j126wybhefgk2lv38uqqiur11u26q275jk3h2ucithd59awpaenqpqi1pszh52179zw0ddqtbrvo6kyrrgv8c34pqrp83j8estjp63v29t4hqp9yg2hhzjlq1e9zqx6gh20n9lsttimz3nbq060ritrphxaru7quwmv3oujhd9xjddpbacq4bnpf270znhgto59yn0980itylf95pxw9x7rvkvi7mfql1sx46puo8rg4dq0>.base(2)}

Based on Benjamin Urquhart's Java solution.

Uses a straight stream of 0 and 1 characters. The link below has some code to prettify the output.

Try it online!

[C++ (VC++)(but tested with gcc as well)], 585 bytes

#define l(x,y)for(int x=0;x<y;x++)
void f(){const char*a="02A800505012Y595Y240U180YD0Y1A0Y540YF80V61C618800321A3186BEFBEF80X10Y40W20YFC001F0X1861C620200868639AFBEFBE0W40C0100180Z83003F0607C00C001008041030101860400C430Z19800310C018604040804101804403008802020808080800600C030047580080800107C002174B604E4FEE1C1B80283B20507E40A0C08360U3820Z751554E00AA0Z140ZF80Z7FC00380E00C0060340160CC06611414422448804510Z8420010040Z940079F4F0";int x=1679;l(i,365){int d=a[i],c=0;d-=(d>47&d<58)?48:((d>64&d<71)?55:0);if(d>70&d<91)c=91-d,d=a[i-1];for(c;c>=0;c--)l(j,4){if(x--)cout<<(int)((d&(8>>j))>0);}}}

Try it online!

ungolfed Version (lacks the break after the 1679th element though and goes until the 1680th):

#include <stdio.h>
#include <iostream>
using namespace std;
int main()
{
    const char arecibo[]="02A800505012Y595Y240U180YD0Y1A0Y540YF80V61C618800321A3186BEFBEF80X10Y40W20YFC001F0X1861C620200868639AFBEFBE0W40C0100180Z83003F0607C00C001008041030101860400C430Z19800310C018604040804101804403008802020808080800600C030047580080800107C002174B604E4FEE1C1B80283B20507E40A0C08360U3820Z751554E00AA0Z140ZF80Z7FC00380E00C0060340160CC06611414422448804510Z8420010040Z940079F4F0";
    int i = 0,j;
    while (i<sizeof(arecibo)-1)
    {   
        char digit = arecibo[i];
        int count=0;
        if (digit >= '0' & digit <= '9')
        {
            digit -= '0';
        }
        else if (digit>='A'& digit<='F')
        {
            digit -=  'A'-10;
        }
        else if (digit > 'F'&digit<='Z')
        {
            //digit does not contain any valid hex digit in this case
            count = 'Z' - digit+1; //digit = Z means repeat 2 more times...
            digit = arecibo[i - 1];
        }
        for (count; count >= 0; count--)
        {
            for (j = 0; j<4; j++)
            {
                cout << (int)(((digit)&(8 >> j))>0);
            }
        }
        i++;
    }
    return 0;
}

as an Explanation: i concatenated the 73 lines of sample output given to one long line. i encoded them in hexadecimal where the bit order is msbfirst (using this program https://github.com/Marc-Bender/longBinaryStreamToHex/releases/download/addedErrorCode-4/longBinaryStreamToHex.exe) i shortened the Output of that by about 70 hexadecimal Digits by using the letters 'G'-'Z' as a sign to repeat the last Digit for a certain amount of times (Z = 2more times, Y = 3more times …) the rest should be relatively self explainatory for Code-Golfers. abusing the preprocessor to shorten loops, abusing the , Operator and the like.

Output Format is uninterrupted stream of 1679 0/1-values.

C# (Visual C# Interactive Compiler), 366 332 329 319 bytes

int i;foreach(var g in"*ЀʂЄ࢈ҲપԤ␀␀␀؀ȀȀȀ؀␀␀సؘࠀƐഘؚ྾ߟ␀␀Ā␀␀ྀ␀␀రܘࠈഌΚ྾ߟ␀␀ă␀ྃ␀ȁăÃ1`ƀ1`ÃĂȃЃЁȂĀ`ÀƀȺ؀Ȃ␀ȏЀȗɛ'Ŀஇ7;ȅ?ȅ0ȍЀ␀␀΂␀ΨՕ΀Ŕ␀ŀЀ?܀àǀƀ`̀°٠Ƙѐʈш҈EB@Ѐޟɸ")Write(Convert.ToString(g,2).PadLeft(12-i++%2,'0'));

Replace all instances of ␀ with \0 to test.

Try it online!

C# (Visual C# Interactive Compiler), 305 bytes, 210 chars

_=>"*ЀʂЄ࢈ҲપԤ␀␀␀؀ȀȀȀ؀␀␀సؘࠀƐഘؚ྾ߟ␀␀Ā␀␀ྀ␀␀రܘࠈഌΚ྾ߟ␀␀ă␀ྃ␀ȁăÃ1`ƀ1`ÃĂȃЃЁȂĀ`ÀƀȺ؀Ȃ␀ȏЀȗɛ'Ŀஇ7;ȅ?ȅ0ȍЀ␀␀΂␀ΨՕ΀Ŕ␀ŀЀ?܀àǀƀ`̀°٠Ƙѐʈш҈EB@Ѐޟɸ".Select((g,i)=>Convert.ToString(g,2).PadLeft(12-i%2,'0'))

Same with above, replace with ␀ with \0 to test. Output as IEnumerable<string>.

Try it online!(Courtesy of Jo King)

05AB1E, 215 210 200 bytes

Saved 15 bytes thanks to Magic Octopus Urn

•cOž¤4é57ñΛ\Ö₃BαöĀíL½₅üBdoÙRθLγ¨G×Tćú$G(˜ƒ¦!€R»SDrµCnJ†d∊ζ·<8‡T@|‹ï=BζćósxG\ÙÎ$¿o₁5/ÔŸÇBûXé-”a::Ž]°∊y;ζ]MÜβ‘иL”β{üÃÇíäc€÷›ÎU=}¨иaŸdY`»¾ÚUβ:ô©¦β†₅DGŠβ3Jêθ,äá!ícqšVÖ›lÈΣ¯pε €êʃDpÙ/¬Žλ8:ãÿ3=€.Þć•3BY¾4×:

Try it online! or with Additional formatting

Base-255 encoded trinary string with occurrences of 0000 replaced by 2.

Ruby, 362 bytes

puts"5r0afnfm8wyke8tfy1pwt7xnuaxyh3wodfp7bhsdufyw0xbdp1pumrz2xir652tuc0ss9oec8yad9vefivd66j126wybhefgk2lv38uqqiur11u26q275jk3h2ucithd59awpaenqpqi1pszh52179zw0ddqtbrvo6kyrrgv8c34pqrp83j8estjp63v29t4hqp9yg2hhzjlq1e9zqx6gh20n9lsttimz3nbq060ritrphxaru7quwmv3oujhd9xjddpbacq4bnpf270znhgto59yn0980itylf95pxw9x7rvkvi7mfql1sx46puo8rg4dq0".to_i(36).to_s(2).rjust(1679,?0)

Integer written in base 36. There's surely a more efficient way to compress the integer, e.g. with zlib or base64.

Try it online!

Bash, 702 697 bytes

xxd -r -p<<X|xz -dc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X

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bash + GNU tools, 351 bytes

base64 -d<<<H4sIAPnNrVwCA6WUCRLDIAwDv8T+/3NNG4wvkTBTcisGSyA8xrcxj9Ds02F+Z7yuf3hnPyz0vYEGz+FG3IKBs+x3oL2PSh0TM/PnaGamft9nPUCew3uCp5RBWdRKGz+qNJn8qRKkkNaTBgeVIFXWOdi8VCaIeUnsfHo6TXpaFa3H5olf6J5MuIHLoEi0uKcRFCvEXG4xseglKzZg7kpYJSLMA3M7wXKR+/L2WiK0kvg+TDASLp6Co1KEVIlVmFzhCktRhBBDdSZYU1xKHrmDUllcWpNR/YNW2QNcHtF0rSySb0MXk/SDUgEwG5gfLvQDxuEdDo8GAAA=|gunzip

TIO

Bubblegum, 275 236 bytes

00000000: e006 8e00 e45d 0018 6988 6507 a228 f86f  .....]..i.e..(.o
00000010: f042 c62f d4d7 b99e 38bc 56c4 52e8 2630  .B./....8.V.R.&0
00000020: 8aaa 7252 d47d 5ef4 c96a 511f 6842 423f  ..rR.}^..jQ.hBB?
00000030: 4532 ca9f 22d3 1633 e0c4 665a d5dc 4e68  E2.."..3..fZ..Nh
00000040: 7b09 76ae 3c7e f9d4 fa4a 05e0 4163 c580  {.v.<~...J..Ac..
00000050: c585 a383 2396 4ca9 1f48 a4b9 744e 37c8  ....#.L..H..tN7.
00000060: 68c5 af23 645d 59a7 542a e6d1 23b9 3aba  h..#d]Y.T*..#.:.
00000070: f0e6 2738 dfd5 b0a3 c6a3 60bf c5b6 5ae6  ..'8......`...Z.
00000080: 7893 30a8 ae04 edf9 298b b777 4d56 285b  x.0.....)..wMV([
00000090: cb74 07cc 7a7b a399 3dc7 c6e7 b693 e715  .t..z{..=.......
000000a0: d908 876e 001f 7408 3c6a 5fcd 37cb 02c4  ...n..t.<j_.7...
000000b0: 93de 33c2 a11e 5bac cd12 d99a fac3 e0fa  ..3...[.........
000000c0: 5268 94f7 d640 0f73 cede f79d 821f 39d1  Rh...@.s......9.
000000d0: dc49 ff06 6962 6c31 dc29 a077 01c3 7690  .I..ibl1.).w..v.
000000e0: 85ef bbec 31d7 5c7f f9fc 8c00            ....1.\.....

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Python 2, 336 bytes

print bin(int('gVQAKCgJERLKqqkgAAAAAMAABoAADQAAKgAAfAAAAAMOMMQAGQ0Yw19998AAAAgAAgAAABAAB+AA+AAADDDjEBAENDHNffffAAAAIGAIAMAAQYAfgwPgBgAIBAIIGAgMMCAGIYAAzAAYhgDDAgIEAggMAiAYBEAQEEBAQEADAGAYAjrABAQACD4AELpbAnJ/cODcAUHZAoPyBQYEGwAAAAAcEAA6iqpwBVAACgAHwAA/4AHAcAYAMBoAsGYDMIoKIRIkQCKIAEIQAIAgAEoAPPp4'.decode('base64').encode('hex'),16))[3:]

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Prints a string of bytes

Node.js, 333 bytes

Returns a binary string of 1,679 characters.

_=>Buffer(")SI)=.);1K?>>>2333A3,93/I3>3)g33)AEAAI)5JQZJTddda3)*3*33+3,e)*e3)//0/1+)1C/7Cgggg3395)9)A3IY)h*IH),39+)995*)AA-)59Y)*O3Z,)//*)91**)A*-)Y+1)I11+)I1)/)5)Y*0?)+)I)-0Y)1@;_*7<gaE/a)Q7[*9HM+IY16I33)a1)*^.><I+S3.38I)*hY)7)a)Y)A,9*A5Y/A:9=9K:1I-=9)19I)9*329)GH<").map(x=>s+=(x-51&&x-41).toString(2).padStart(x-51?6:12,0),s='')&&s

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JavaScript (ES8), 413 bytes

Returns a binary string of 1,679 characters.

_=>atob('AsKoAFBQEiIlwpVVUk!!ABwo!DQ!Gg!V!Aw7g!!GHGHCi!yGjHChsK+w7vDr8K!!Q!Q!!g!/DgAHDs!AGGHDhiAgCGhjwprDu8Ovwr4!ABAw4AQAcK!MKDAD8GB8OAD!QCAQQMBAYYEAMQwABwpgAMQwBwoYEBAgEEBgEQDAIwoAgIMKAwoDCgMKABgDDgDAEdcKACAgAEHwAIXTCtgTDpMO+w6HDgcK4AsKDwrIFB8OkCgwINg!!A4IAB1FVTDoArCo!U!/CgAB/w4ADwoDDoAwAYDQBYMOMBmEUFEIkSMKARR!woQgAQB!MKUAHnDtA'.split`!`.join`AA`).replace(/[\s\S]/g,c=>c.charCodeAt().toString(2).padStart(8,0))

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Wolfram Language (Mathematica), 383 bytes

StringPartition[Uncompress@"1:eJylVNsRwjAM44s92KBaBTZgAUZhZXqtHUuOWrgjfSRRHFlO4tyer/vjfb1clq0gHirZLRjby986hppcT5p+L3BmgJ3t4Ul4GsNyG++7YbaXLh0ZTPhXa4Sn+X/s9Qfk3Hx2cOaSIuNYaVu5laschvgzSqAjHeZBhilKgKBDEhw0upJRg+HOK4MyNC29sfbc3RV0VPDqeLiRTsG1ulExq1IitpunOa7asnYM9siDZ6eidUCkEzBOUbCkGIig4aTyUGBYWAX6W6aXIWGGI/HlhmsqzSU0QTZjkMVpaX5sBsm1OGKVg1qdjKP0EdyqZBRLhukn8DLBQav6kccgz8OKfgBzjj6Z",23]

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Perl 6, 368 bytes

.say for :36('FJXOE0PDDNF5Y5EHGB8M9SWMXQOXIKIT9F6ZKWWDEACHCBGXL1N2H60CN0CJ4EMKF7D6MODSKYJVNR4SFTDR6NSM421LQ67B6MWF0G5BQATFOJJJBQ0UFQM64T0MWSQN41C4S5D1QR5KJM2L9UTYMMKUBBQWY45YCMRGO8ZRGTQH7LXMZBUASLCTKX30IH0AYKYEPHO8HFHX8GAY5WM38YOSUX0HABYSH2PPBLRDRZIN5ANAQ3V8PLOZ6EHC0UI95EVJVYD1820T6J14HGX85NWFQET2NWOMSNUT0JW4LHMY90X094TEE9KXJXSNN6YPERFQW').base(2).substr(1).comb(23)

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The long string is the message as a single base-36 number (with a single prefixed 1 bit to preserve the leading zeroes) which is then converted back to binary and printed 23 bits at a time.

Jelly, 213 bytes

“H²ɓ¶Ṡḷ€ẹ]ƒf*ḳḢ&ƁṇOḥ{ḄṫwỊ+oLạʋߢH9¢¹÷ỴɗÇ⁶ƲƙæḊẋ3³=1!VƇƁ'D⁺3Ỵɱ©⁵%fȯez#ƈjƒżṆo.ZF⁶ċṢ⁶ọṛb9Ȯƒd?ƁUĠt4ẇ,ḞġƒµƭfʠƁP§÷øȤŻPɲẋ(¢ß¢(⁽3¶ṙėɗy@ṁYȮL~e⁷ƤĊ§nỊṅµṠ°@7ẠB>Ġ⁻İ}uy¡½:esOpḢt}qS©HÞṬĖṛṇḣ9÷;ESḢ,Ẉ^ṙpƲ©tṃwçnẒṆ¡⁻Jıƒị£-&Ɱ*ẋʂżoȯÑḢɼ’

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I played around with Huffman coding, but the improvements in data size were outweighed by the extra code. As such, this is simply a base-250 encoded version of the desired output. Output consists of an integer that when decoded as bijective base 2 will yield the 1D list of 1s and 2s. Thanks @Emigna for pointing out the change in rules.

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If a more conventional binary encoding is preferred, here is one that encodes an integer representation of the inverted binary message. The most significant bit of the integer represents the beginning of the message.

Perl 5, 460 bytes

printf"%023b",oct"0x$_"for qw/15400 141404 4444b2 555524 0 600 1a00 1a00 2a00 3e00 0 61c618 400190 68c61a 7df7df 0 80002 0 40001 7c001f 0 618718 404010 68639a 7df7df 0 81802 1800 41801 7c181f 1800 100804 81808 61810 18860 1980 18860 61810 81008 101804 201804 200808 101010 80060 60180 11d600 101000 107c00 10ba5b 1393f 5c3837 283b 10283f 102830 106c00 0 1c1000 1d4555 1c0154 140 7c00 1ff00 701c0 c0060 1a00b0 330198 228288 224488 22880 21080 20080 9400 3cfa78/

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