Generator matrices of distance optimal binary codesTopPreliminaries: Methods, NotationTables for binary codes

Tables for binary codes

In the case q=2 we computed:

Tnk2
n\k12345678910111213141516171819202122232425
11111111111111111111111111
21222222222222222222222222
31344444444444444444444444
41478888888888888888888888
5151115161616161616161616161616161616161616161616
6171930353636363636363636363636363636363636363636
7182956737980808080808080808080808080808080808080
811044107161186193194194194194194194194194194194194194 194194194194194194
911266200363462497505506506506506506506506506506506506 506506506506506506
101149637283712221392143914481449144914491449144914491449 144914491449144914491449144914491449
11116136680196334354282455946204630463146314631463146314631 463146314631463146314631463146314631
1211919312414721103971480516580170161709417105171061710617106 1710617106171061710617106171061710617106171061710617106
13121265222111477335785787570491740487471074807748197482074820 7482074820748207482074820748207482074820748207482074820
14124361393828220115624258894361339396281403171404150404269404282 404283404283404283404283404283404283404283404283404283404283 404283404283
15127485688069692419789132128022786372706897280107428140222815436 281558028155942815595281559528155952815595281559528155952815595 2815595281559528155952815595
161306431186017196615852177.57049517.74506124.33759926.116298 26.36418626.38789326.38989426.39006626.39008126.390082 26.39008226.39008226.39008226.39008226.39008226.390082 26.39008226.39008226.390082
17133841201484219726.13013047.305333166.540680289.965315 336.319805343.646556344.285051344.327452344.330232344.330435 344.330451344.330452344.330452344.330452344.330452344.330452 344.330452344.330452344.330452344.330452
18137109333778102581123.928972311.7422561794.0401684441.066380 6005.6137246334.0733406363.9014286365.5126496365.586927 6365.5907316365.5909696365.5909866365.5909876365.5909876365.590987 6365.5909876365.5909876365.5909876365.5909876365.590987
19140140155814246214393.1615412103.02572620987.47644782142.254402 144461.760657164622.945438166938.366078167057.901531167061.886396 167062.014031167062.019160167062.019436167062.019454167062.019455 167062.019455167062.019455167062.019455167062.019455167062.019455 167062.019455
201441782910075.821962358.57099714206.632939254684.454328 1.707902.1514634.410619.0914395.907271.8441086.165900.986093 6.181973.7692776.182443.6474366.182453.3088436.182453.524342 6.182453.5311706.182453.5314886.182453.5315076.182453.531508 6.182453.5315086.182453.5315086.182453.5315086.182453.531508 6.182453.531508
21148224814639213.5401521356.17899194726.1674273.107605.995993 37.600720.702701158.540306.553453280.729391.647046316.478681.285034 319.736342.193643319.845432.216228319.847239.002271319.847261.968213 319.847262.326118319.847262.335103319.847262.335467319.847262.335487 319.847262.335488319.847262.335488319.847262.335488319.847262.335488 319.847262.335488
22152281123245830.9422305021.267644618051.90498337.418101.305011 841.501320.1550686251.420890.82665316593.022336.71819322090.637877.776663 22927.457506.43614222967.421846.75634322968.142624.77742822968.149408.495125 22968.149462.02669522968.149462.61204722968.149462.62374422968.149462.624158 22968.149462.62417922968.149462.62418022968.149462.62418022968.149462.624180 22968.149462.624180
23156348736446269.44349218160.0795083.927156.178649439.995775.004885 18681.874482.499450256404.023517.2960481.133708.193551.906989 2.015944.045461.7378852.258359.726818.7428962.277401.625105.496912 2.277877.045034.0060102.277881.669817.8008222.277881.694661.444763 2.277881.694783.8257162.277881.694784.7692842.277881.694784.784361 2.277881.694784.7848292.277881.694784.7848512.277881.694784.784852 2.277881.694784.7848522.277881.694784.784852
241614301564560153.03839764086.74826724.243834.6191575025.781692.126252 405931.192946.99742210.572897.056655.02403383.806992.795597.973727 226.289469.878102.289357300.168079.319920.273349310.559218.986277.810406 310.978730.227200.609356310.984203.275990.526408310.984232.062431.556094 310.984232.151139.830875310.984232.151414.324690310.984232.151415.825086 310.984232.151415.844348310.984232.151415.844875310.984232.151415.844898 310.984232.151415.844899310.984232.151415.844899
251655263864230331.208859220608.700157145.277300.34358555627.454599.068011 8.573731.168352.587920429.852229.059302.2696366387.295315.807525.889647 29090.805184.251551.14731851863.563434.039137.77092557884.718164.365471.348317 58315.986896.511523.69592058324.919509.928342.50768458324.980440.974683.278272 58324.980614.753882.24151658324.980615.062715.53375858324.980615.063319.811943 58324.980615.063322.16706658324.980615.063322.19146658324.980615.063322.192056 58324.980615.063322.19208058324.980615.063322.192081

Snk2
n\k12345678910111213141516171819202122232425
11000000000000000000000000
21100000000000000000000000
31210000000000000000000000
41331000000000000000000000
51464100000000000000000000
6161211510000000000000000000
71721271761000000000000000000
819346354257100000000000000000
9111541341639935810000000000000000
10113822764653851704791000000000000000
11115120544128314728472776110100000000000000
1211817410483480567644081775436781110000000000000
1312024419569256221012429712616355766297121000000000 000
14123337357724282874041432701024453494268909791191310000 0000000
1512645863956281235009790149195735742826094177129481414 1441410000000000
16129613112171601061.4132515.98527810.1745666.5925381778699 247888237072001172151000000000
17132808193074018245.70815841.175203119.235347123.424635 46.3544907.32675163849542401278020316100000000
1813610563268599203322.903161287.8132841482.2979122647.026212 1564.547344328.45961629.828088161122174278380423817100 00000
191391361544132.40632990.6993982009.86418518884.45072161154.777955 62319.50625520161.1847812315.420640119.5354533.984865127635 5129276181000000
201431738892255.730955352.74903513848.061942240477.821389 1.453217.6971352.702716.9399761.496652.752669258629.14198516072.783184 469.8781599.661407215499682831819100000
21147220014414413.3937601342.63883993369.9884363.012879.828566 34.493114.706708120.939585.850752122.189085.09359335.749289.637988 3.257660.908609109090.0225851806.78604322.9659423579058985 3642010000
22151275922964730.7097724990.325414613030.63733936.800049.400028 804.083218.8500575409.919570.67158510341.601445.8915405497.615541.058470 836.819628.65947939.964340.320201720778.0210856783.71769753.531570 58535211697414211000
23155343136097569.07903018090.6360163.908996.099141436.068618.826236 18241.878707.494565237722.149034.796598877304.170034.610941882235.851909.830896 242415.681357.00501119041.898286.754016475.419928.5090984.624783.794812 24843.643941122.3809539435681507746822100
241604240560259152.47383763933.70987024.179747.8708905001.537857.507095 400905.411254.87117010.166965.863708.02661173.234095.738942.949694 142.482477.082504.31563073.878609.441817.98399210.391139.666357.537057 419511.240922.7989505473.048789.91705228.786441.02968688708.274781 274.4938151500396192625272310
251645198858967330.344629220277.491298145.056691.64342855482.177298.724426 8.518103.713753.519909421.278497.890949.6817165957.443086.748223.620011 22703.509868.444025.25767122772.758249.787586.6236076021.154730.326333.577392 431.268732.146052.3476038.932613.416818.81176460931.046340.770588 173.779198.963244308833.292242604.27818523551232440059024 1

Rnk2
n\k12345678910111213141516171819202122232425
11000000000000000000000000
21000000000000000000000000
31100000000000000000000000
41110000000000000000000000
51221000000000000000000000
61353100000000000000000000
7141010410000000000000000000
81518281851000000000000000000
917317171317100000000000000000
10185116525016551810000000000000000
111107936180980936179101000000000000000
1211212175424843759248475412112100000000000000
131141771503724016749167497240150317714100000000000 00
141162542893203417282811366272828203412893254161000000 000000
1511935653935532231123578439078439031123555322539335619100 000000000
16121490977314623713114155.5174769.0991515.5174761311415146237 97734902110000000000
17124661172733767255.44572239.291974112.170248112.170248 39.2919745.44572237672517273661241000000000
181278822986094755522.237612280.2153851434.0406952516.512343 1434.040695280.21538522.2376129475552986088227100000 000
19130115750557232899989.0390271979.34546618548.32132959541.856324 59541.85632418548.3213291979.34546689.039027232899950557 11573010000000
201331501840245.598888348.67655513726.798428238131.628435 1.432719.8344972.638783.8277521.432719.834497238131.62843513726.798428 348.6765555.598888840241501331000000
21137192613722813.1719061332.82425992895.8631192.996684.899641 34.232136.753766119.422430.817457119.422430.81745734.232136.753766 2.996684.89964192895.8631191332.82425913.1719061372281926 37100000
22140244522054230.3428614967.096197611213.59909336.690482.155548 800.809349.7293555373.909271.54828910217.895164.6942825373.909271.548289 800.809349.72935536.690482.155548611213.5990934967.09619730.342861 22054224454010000
23144307334912868.48105818036.6594293.902188.079125435.346012.682054 18201.804726.691491236882.055277.892069871770.543718.727066871770.543718.727066 236882.055277.89206918201.804726.691491435.346012.6820543.902188.079125 18036.65942968.4810583491283073441000
241483834544980151.51276763810.58793324.154847.6604814996.906225.153071 400429.268282.87464810.147883.888977.52609172.990839.957170.583777 141.594707.595183.64836972.990839.957170.58377710.147883.888977.526091 400429.268282.8746484996.906225.15307124.154847.66048163810.587933 151.512767544980383448100
251524740839453328.820214220001.781595144.967854.07894355453.365806.920084 8.512626.030566.797766420.858510.480780.9262925947.032864.996612.384570 22629.388003.003089.36461922629.388003.003089.3646195947.032864.996612.384570 420.858510.480780.9262928.512626.030566.79776655453.365806.920084 144.967854.078943220001.781595328.82021483945347405210

Wnk2
n\k12345678910111213141516171819202122232425
11000000000000000000000000
22100000000000000000000000
33310000000000000000000000
44641000000000000000000000
5510105100000000000000000000
66162216610000000000000000000
772343432371000000000000000000
88327710677328100000000000000000
994313124024013143910000000000000000
10105621351670551621356101000000000000000
11117133310601988198810603337111100000000000000
1212895072108546876645468210850789121000000000000 0
131310975140641472429765297651472440647511091310000000 00000
1414132108876413900611716917303511716939006764110881321410 0000000000
151515815461403610181846726610745261074526467266101818140361546 1581510000000000
161618721592525326192418805177.05980411.2490927.0598041880517 261924252532159187161000000000
17172192967445606637487.58867548.235007130.484439130.484439 48.2350077.58867566374844560296721917100000000
1818255402377245165578130.491836336.0482911612.7823512777.510651 1612.782351336.04829130.491836165578177245402325518100 00000
191929453841316584.062110121.1912342345.91247620497.233072 63932.28860663932.28860620497.2330722345.912476121.191234 4.0621101316585384294191000000
202033771222208839.793065473.94026916193.974418260975.054461 1.517149.9857412.766649.2285821.517149.985741260975.054461 16193.974418473.9402699.793065220883712233720100000
2121384932236502723.1868251816.579108109563.9628543.273854.883027 36.010264.692449123.706235.079334123.706235.07933436.010264.692449 3.273854.883027109563.9628541816.57910823.1868253650279322 3842110000
22224351208159467453.8965976806.904522722594.60019340.073904.283055 840.093483.5425065533.625805.75091910465.307680.9708745533.625805.750919 840.093483.54250640.073904.283055722594.6001936806.90452253.896597 59467412081435221000
232349015512955649122.97562724897.5405384.631590.699334476.142523.109291 19081.972191.037071243255.774840.547517887769.477715.581815887769.477715.581815 243255.774840.54751719081.972191.037071476.142523.1092914.631590.699334 24897.540538122.9756279556491551249023100
2424550197521515908275.44946488831.25040828.811338.5702245477.680380.616386 419987.383445.90824110.410221.638548.57412874.121865.216658.531509 143.370246.560219.89744574.121865.216658.53150910.410221.638548.574128 419987.383445.9082415477.680380.61638628.811338.57022488831.250408 275.4494641515908197525502410
2525614249502374875605.794093309108.741706173.868030.21365260959.857679.340812 8.938091.097199.428150431.688719.529498.2558446031.564951.964882.151520 22846.880115.004245.15511622846.880115.004245.1551166031.564951.964882.151520 431.688719.529498.2558448.938091.097199.42815060959.857679.340812 173.868030.213652309108.741706605.79409323748752495061425 1

bar (T)nk2
n\k123456789101112
1111111111111
2011111111111
3012222222222
4002333333333
5001455555555
60015910101010101010
700161419202020202020
800062135414242424242
90005347294101102102102102
10000450155235267275276276276
11000367340652803847856857857
12000291791207628973163322232323233
130001113190775391263714585150251510115112
1400011294708315006869186625909139160891704
15000114511780149273469936683709741393750287751346
160000145292367746493.9607327.2370398.3471288.5200938.537672
170000129707294.21579339.015186100.286768130.154074135.491050 135.981479
18000011316481823.147524420.3798461716.8406902749.120246 2999.1234093023.267823
19000091366180124.7986414683.45421033715.54396275106.429752 90893.68506992850.796595
20000067770299650.06176651982.691288709837.8582372.488146.723882 3.673533.1844263.897691.734385
2100005015282383243.108226562811.23883315.258736.18103293.150518.146069 189.826779.787688221.144290.228666
22000034285257515431.9159405.880254.646284325.041745.327771 3706.690786.42372911814.008741.68836816638.483120.906749
230000215.00282869923.53065358.993186.9954626750.606765.695928 150087.316077.676607827902.856160.2817741.599310.514269.574719
240000148.239590301620.524570567.237565.232590135585.323967.378557 6.021781.479137.41535761.581090.056370.702326185.299679.319527.400995
250000912.7423211.239173.5497115225.887244.0236512.624219.225117.097086 235.969872.324575.0118524662.313565.324908.60003424196.368363.140918.426653

bar (S)nk2
n\k123456789101112
1100000000000
2010000000000
3011000000000
4002100000000
5001310000000
6001441000000
7001585100000
800061514610000
9000529382271000
1000044610580328100
1100036427331215144910
12000289700128582126659101
13000111217945632509819484407611
1400011284579267923719117934428869596
150001144116351374933206632137735768488941059
1600001452909174541331860833276307111008917296517579
170000129706004.14506434.79939361.27158229.8673065.336976 490429
18000011316470522.982706397.2323221296.4608441032.279556 250.00316324.144414
19000091366089124.4324614558.65556929032.08975241390.885790 15787.2553171957.111526
20000067770232649.29146751332.629522657855.1669491.778308.865645 1.185386.460544224158.549959
210000501.5281883241.579988559568.13060714.695924.942199 77.891781.96503796.676261.64161931.317510.440978
220000342.85254115429.0633655.864822.730344319.161490.681487 3381.649041.0959588107.317955.2646394824.474379.218381
230000215.00280769918.52782558.923263.4648096691.613578.700466 143336.709311.980679677815.540082.605167771407.658109.292945
240000148.239576301612.284980566.935944.708020135018.086402.145967 5.886196.155170.03680055.559308.577233.286969123.718589.263156.698669
250000912.7423121.239160.8073905224.648070.4739402.618993.337873.073435 233.345653.099457.9147664426.343693.000333.58818219534.054797.816009.826619

bar (R)nk2
n\k123456789101112
1100000000000
2000000000000
3010000000000
4001000000000
5001100000000
6001210000000
7001431000000
8000594100000
900052219610000
10000440703571000
11000360220190599100
12000286629977466961110
1300011101700487536891041147131
1400011274463249203123312476217821815
15000114311505132811293070175114388234326314
16000014428946733654304663129494798906681131238223
170000129704544.11583634.04916858.05734326.5514934.207507 312785
18000011316457522.911956393.0753161261.520643970.677928 219.91333818.746245
19000091365976124.2676074535.64340428634.10404040091.199028 14751.6434881705.968487
20000067770141648.92524651208.126040653292.3469771.749241.790421 1.143933.881618208341.125723
2100005015281213240.809641558918.67398814.644569.28286777.233528.615181 94.896652.49548830.131087.673329
22000034285249115427.5350855.861580.783823318.601798.004832 3366.948552.3686828029.397101.5210994727.756657.299913
230000215.00277369915.67521758.907833.6308066685.748106.411607 143017.496460.548526674433.232743.798009763298.560436.846310
240000148.239555301607.282123566.866024.651659134959.159896.496856 5.879503.981871.05245455.415957.166965.834098123.040695.800378.907768
250000912.7422981.239152.5677805224.346455.3361392.618426.386497.998000 233.210629.147434.9553024420.457177.627168.39242819478.492106.895607.118312


harald.fripertinger@uni-graz.at,
last changed: December 1, 2003

Generator matrices of distance optimal binary codesTopPreliminaries: Methods, NotationTables for binary codes