05AB1E, 215 210 200 bytes

Saved 15 bytes thanks to Magic Octopus Urn

•cOž¤4é57ñΛÖ₃BαöĀíL½₅üBdoÙRθLγ¨G×Tćú$G(˜ƒ¦!€R»SDrµCnJ†d∊ζ·<8‡T@|‹ï=BζćósxGÙÎ$¿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×:

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or with Additional formatting

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

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.

Try it online - with further decoding to demonstrate output!

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.

Java, 688 678 590 379(!) bytes

Returns a string.

n->"000000"+new java.math.BigInteger("5r0afnfm8wyke8tfy1pwt7xnuaxyh3wodfp7bhsdufyw0xbdp1pumrz2xir652tuc0ss9oec8yad9vefivd66j126wybhefgk2lv38uqqiur11u26q275jk3h2ucithd59awpaenqpqi1pszh52179zw0ddqtbrvo6kyrrgv8c34pqrp83j8estjp63v29t4hqp9yg2hhzjlq1e9zqx6gh20n9lsttimz3nbq060ritrphxaru7quwmv3oujhd9xjddpbacq4bnpf270znhgto59yn0980itylf95pxw9x7rvkvi7mfql1sx46puo8rg4dq0",36).toString(2)

-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!)

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Explanation:

n->"000000"                                                  // Padding

   +new java.math.BigInteger("base36 string",36)             // Decode the base-36 integer.

   .toString(2)                                              // Re-encode as binary

                                                             // Implicit return

Brainfuck, 2360 2008 bytes

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

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I will probably golf this further soon.

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.

Wolfram Language (Mathematica), 383 bytes

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

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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 to test.

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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 to test. Output as IEnumerable<string>.

Try it online!(Courtesy of Jo King)

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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Deadfish~, 1115 bytes

ooooooiodoiodoiodoiod{o}{i}c{d}ooiodoiodoooooiodoiodoooooooiodoo{i}c{d}iodoooiodoooiodoooiodooiodoioodooiodo{i}c{d}iodoiodoiodoiodoiodoiodoiodoiodooiodooiodoo{i}c{d}{oo}ooo{i}c{d}{o}ooioodooooooooo{i}c{d}{o}ioodoiodooooooooo{i}c{d}{o}ioodoiodooooooooo{i}c{d}oooooooooiodoiodoiodooooooooo{i}c{d}oooooooooiooooodooooooooo{i}c{d}{oo}ooo{i}c{d}ioodooooiooodoooioodooooioodooo{i}c{d}iod{o}oooioodooiodoooo{i}c{d}ioodoiodoooioodoooioodooooioodoiodo{i}c{d}iooooodoiooooodoiooooodoioooood{i}c{d}{oo}ooo{i}c{d}oooiod{o}oooooooiodo{i}c{d}{oo}ooo{i}c{d}ooooiod{o}oooooooiod{i}c{d}ioooood{o}oooioooood{i}c{d}{oo}ooo{i}c{d}ioodooooioodooooiooodoooioodooo{i}c{d}iodoooooooiodoooooooooiodoooo{i}c{d}ioodoiodooooioodoooiooodooioodoiodo{i}c{d}iooooodoiooooodoiooooodoioooood{i}c{d}{oo}ooo{i}c{d}oooiodooooooioodoooooooooiodo{i}c{d}{o}iood{o}o{i}c{d}ooooiodoooooiood{o}iod{i}c{d}iooooodoooooioodooooooioooood{i}c{d}{o}iood{o}o{i}c{d}ooiodooooooooiodooooooooiodoo{i}c{d}oooiodooooooioodoooooooiodooo{i}c{d}ooooioodooooioodooooooiodoooo{i}c{d}ooooooioodoooiodooooioodooooo{i}c{d}{o}ioodooioodooooooo{i}c{d}ooooooioodoooiodooooioodooooo

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If someone has the patience to golf this further, I salute you ahead of time. :P

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(/[sS]/g,c=>c.charCodeAt().toString(2).padStart(8,0))

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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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bash + GNU tools, 351 bytes

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

TIO

Java (OpenJDK 8), 364 bytes

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

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Explanation: First had n->new java.math.BigInteger(str,36).toString(2), just converting a radix 36 number to binary, but that needed nine extra chars for leading zeroes. Then, I got the idea of run-length encoding some zeroes as twos. A length of four zeroes seems to minimize the radix 36 length, so n->new java.math.BigInteger(str,36).toString(3).replaceAll("2","0000")

See the discussion under this answer for the leading zeroes bug fix by @KevinCruijssen

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

Bash, 702 697 bytes

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

fd377a585a000004e6d6b4460200210116000000742fe5a3e006d7010c5d

0018698865079cf6752c9e9a501a87a798b4844f9fcfdaaf87733b9d8239

48c816d860a938767f6cb81299f3e8a638effe3068c0e096a8949c81d706

7dff3ec44e5df185b3a48e5b5857724386e8c37cfbd5c856b12614ee78ec

c41df4db3aea71fd3a8fa474905609f78eb3fd66e246557965e4ab6dfd67

efbd9202f542ded9cf98a6401ee2d23afb2f544bd2442c6f428fd612397c

f2c6ec50847ddccc5832185e487712e5a7676b97058d7e485d5a3536166a

44ab3c689c93073cdda73b5306a83c4cd268e79db238bfa2d08ac912a578

75020bc7828342d5a62ce367aff7fd89290336128d119fa4272da2b2a79f

5973c71935af054f2d91c1bd3ea4847a3502d6dc8c975114dacf8a4de600

622d80986dbb0cd00001a802d80d00001b16e2a7b1c467fb020000000004

595a

X

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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.

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[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);}}}

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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.