{"id":227,"date":"2023-06-08T16:24:01","date_gmt":"2023-06-08T20:24:01","guid":{"rendered":"http:\/\/khaymake.clasit.org\/?page_id=227"},"modified":"2025-03-20T10:12:33","modified_gmt":"2025-03-20T14:12:33","slug":"group-testing-matrix-parameters-from-reed-solomon-codes","status":"publish","type":"page","link":"https:\/\/khaymake.clasit.org\/?page_id=227","title":{"rendered":"Group testing matrix parameters from Reed-Solomon Codes"},"content":{"rendered":"\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t
Alphabet size (q)<\/th>Codeword length (n)<\/th>Code dimension (k)<\/th>Code min dist (d)<\/th>Group test disjunct (D’)<\/th>Samples (N’=q^k)<\/th>Tests (t=qn) <\/th>guaranteed positivity=D’\/N’<\/th>Samples\/tests<\/th>\n<\/tr>\n<\/thead>\n
3<\/td>3<\/td>2<\/td>2<\/td>2<\/td>9<\/td>9<\/td>0.22222222222222<\/td>1<\/td>\n<\/tr>\n
4<\/td>3<\/td>2<\/td>2<\/td>2<\/td>16<\/td>12<\/td>0.125<\/td>1.3333333333333<\/td>\n<\/tr>\n
4<\/td>4<\/td>2<\/td>3<\/td>3<\/td>16<\/td>16<\/td>0.1875<\/td>1<\/td>\n<\/tr>\n
4<\/td>4<\/td>3<\/td>2<\/td>1<\/td>64<\/td>16<\/td>0.015625<\/td>4<\/td>\n<\/tr>\n
5<\/td>3<\/td>2<\/td>2<\/td>2<\/td>25<\/td>15<\/td>0.08<\/td>1.6666666666667<\/td>\n<\/tr>\n
5<\/td>4<\/td>2<\/td>3<\/td>3<\/td>25<\/td>20<\/td>0.12<\/td>1.25<\/td>\n<\/tr>\n
5<\/td>4<\/td>3<\/td>2<\/td>1<\/td>125<\/td>20<\/td>0.008<\/td>6.25<\/td>\n<\/tr>\n
5<\/td>5<\/td>2<\/td>4<\/td>4<\/td>25<\/td>25<\/td>0.16<\/td>1<\/td>\n<\/tr>\n
5<\/td>5<\/td>3<\/td>3<\/td>2<\/td>125<\/td>25<\/td>0.016<\/td>5<\/td>\n<\/tr>\n
5<\/td>5<\/td>4<\/td>2<\/td>1<\/td>625<\/td>25<\/td>0.0016<\/td>25<\/td>\n<\/tr>\n
7<\/td>3<\/td>2<\/td>2<\/td>2<\/td>49<\/td>21<\/td>0.040816326530612<\/td>2.3333333333333<\/td>\n<\/tr>\n
7<\/td>4<\/td>2<\/td>3<\/td>3<\/td>49<\/td>28<\/td>0.061224489795918<\/td>1.75<\/td>\n<\/tr>\n
7<\/td>4<\/td>3<\/td>2<\/td>1<\/td>343<\/td>28<\/td>0.0029154518950437<\/td>12.25<\/td>\n<\/tr>\n
7<\/td>5<\/td>2<\/td>4<\/td>4<\/td>49<\/td>35<\/td>0.081632653061224<\/td>1.4<\/td>\n<\/tr>\n
7<\/td>5<\/td>3<\/td>3<\/td>2<\/td>343<\/td>35<\/td>0.0058309037900875<\/td>9.8<\/td>\n<\/tr>\n
7<\/td>5<\/td>4<\/td>2<\/td>1<\/td>2401<\/td>35<\/td>0.00041649312786339<\/td>68.6<\/td>\n<\/tr>\n
7<\/td>6<\/td>2<\/td>5<\/td>5<\/td>49<\/td>42<\/td>0.10204081632653<\/td>1.1666666666667<\/td>\n<\/tr>\n
7<\/td>6<\/td>3<\/td>4<\/td>2<\/td>343<\/td>42<\/td>0.0058309037900875<\/td>8.1666666666667<\/td>\n<\/tr>\n
7<\/td>6<\/td>4<\/td>3<\/td>1<\/td>2401<\/td>42<\/td>0.00041649312786339<\/td>57.166666666667<\/td>\n<\/tr>\n
7<\/td>6<\/td>5<\/td>2<\/td>1<\/td>16807<\/td>42<\/td>5.9499018266199E-5<\/td>400.16666666667<\/td>\n<\/tr>\n
7<\/td>7<\/td>2<\/td>6<\/td>6<\/td>49<\/td>49<\/td>0.12244897959184<\/td>1<\/td>\n<\/tr>\n
7<\/td>7<\/td>3<\/td>5<\/td>3<\/td>343<\/td>49<\/td>0.0087463556851312<\/td>7<\/td>\n<\/tr>\n
7<\/td>7<\/td>4<\/td>4<\/td>2<\/td>2401<\/td>49<\/td>0.00083298625572678<\/td>49<\/td>\n<\/tr>\n
7<\/td>7<\/td>5<\/td>3<\/td>1<\/td>16807<\/td>49<\/td>5.9499018266199E-5<\/td>343<\/td>\n<\/tr>\n
7<\/td>7<\/td>6<\/td>2<\/td>1<\/td>117649<\/td>49<\/td>8.4998597523141E-6<\/td>2401<\/td>\n<\/tr>\n
8<\/td>3<\/td>2<\/td>2<\/td>2<\/td>64<\/td>24<\/td>0.03125<\/td>2.6666666666667<\/td>\n<\/tr>\n
8<\/td>4<\/td>2<\/td>3<\/td>3<\/td>64<\/td>32<\/td>0.046875<\/td>2<\/td>\n<\/tr>\n
8<\/td>4<\/td>3<\/td>2<\/td>1<\/td>512<\/td>32<\/td>0.001953125<\/td>16<\/td>\n<\/tr>\n
8<\/td>5<\/td>2<\/td>4<\/td>4<\/td>64<\/td>40<\/td>0.0625<\/td>1.6<\/td>\n<\/tr>\n
8<\/td>5<\/td>3<\/td>3<\/td>2<\/td>512<\/td>40<\/td>0.00390625<\/td>12.8<\/td>\n<\/tr>\n
8<\/td>5<\/td>4<\/td>2<\/td>1<\/td>4096<\/td>40<\/td>0.000244140625<\/td>102.4<\/td>\n<\/tr>\n
8<\/td>6<\/td>2<\/td>5<\/td>5<\/td>64<\/td>48<\/td>0.078125<\/td>1.3333333333333<\/td>\n<\/tr>\n
8<\/td>6<\/td>3<\/td>4<\/td>2<\/td>512<\/td>48<\/td>0.00390625<\/td>10.666666666667<\/td>\n<\/tr>\n
8<\/td>6<\/td>4<\/td>3<\/td>1<\/td>4096<\/td>48<\/td>0.000244140625<\/td>85.333333333333<\/td>\n<\/tr>\n
8<\/td>6<\/td>5<\/td>2<\/td>1<\/td>32768<\/td>48<\/td>3.0517578125E-5<\/td>682.66666666667<\/td>\n<\/tr>\n
8<\/td>7<\/td>2<\/td>6<\/td>6<\/td>64<\/td>56<\/td>0.09375<\/td>1.1428571428571<\/td>\n<\/tr>\n
8<\/td>7<\/td>3<\/td>5<\/td>3<\/td>512<\/td>56<\/td>0.005859375<\/td>9.1428571428571<\/td>\n<\/tr>\n
8<\/td>7<\/td>4<\/td>4<\/td>2<\/td>4096<\/td>56<\/td>0.00048828125<\/td>73.142857142857<\/td>\n<\/tr>\n
8<\/td>7<\/td>5<\/td>3<\/td>1<\/td>32768<\/td>56<\/td>3.0517578125E-5<\/td>585.14285714286<\/td>\n<\/tr>\n
8<\/td>7<\/td>6<\/td>2<\/td>1<\/td>262144<\/td>56<\/td>3.814697265625E-6<\/td>4681.1428571429<\/td>\n<\/tr>\n
8<\/td>8<\/td>2<\/td>7<\/td>7<\/td>64<\/td>64<\/td>0.109375<\/td>1<\/td>\n<\/tr>\n
8<\/td>8<\/td>3<\/td>6<\/td>3<\/td>512<\/td>64<\/td>0.005859375<\/td>8<\/td>\n<\/tr>\n
8<\/td>8<\/td>4<\/td>5<\/td>2<\/td>4096<\/td>64<\/td>0.00048828125<\/td>64<\/td>\n<\/tr>\n
8<\/td>8<\/td>5<\/td>4<\/td>1<\/td>32768<\/td>64<\/td>3.0517578125E-5<\/td>512<\/td>\n<\/tr>\n
8<\/td>8<\/td>6<\/td>3<\/td>1<\/td>262144<\/td>64<\/td>3.814697265625E-6<\/td>4096<\/td>\n<\/tr>\n
8<\/td>8<\/td>7<\/td>2<\/td>1<\/td>2097152<\/td>64<\/td>4.7683715820312E-7<\/td>32768<\/td>\n<\/tr>\n
9<\/td>3<\/td>2<\/td>2<\/td>2<\/td>81<\/td>27<\/td>0.024691358024691<\/td>3<\/td>\n<\/tr>\n
9<\/td>4<\/td>2<\/td>3<\/td>3<\/td>81<\/td>36<\/td>0.037037037037037<\/td>2.25<\/td>\n<\/tr>\n
9<\/td>5<\/td>2<\/td>4<\/td>4<\/td>81<\/td>45<\/td>0.049382716049383<\/td>1.8<\/td>\n<\/tr>\n
9<\/td>5<\/td>3<\/td>3<\/td>2<\/td>729<\/td>45<\/td>0.0027434842249657<\/td>16.2<\/td>\n<\/tr>\n
9<\/td>5<\/td>4<\/td>2<\/td>1<\/td>6561<\/td>45<\/td>0.00015241579027587<\/td>145.8<\/td>\n<\/tr>\n
9<\/td>6<\/td>2<\/td>5<\/td>5<\/td>81<\/td>54<\/td>0.061728395061728<\/td>1.5<\/td>\n<\/tr>\n
9<\/td>6<\/td>3<\/td>4<\/td>2<\/td>729<\/td>54<\/td>0.0027434842249657<\/td>13.5<\/td>\n<\/tr>\n
9<\/td>6<\/td>4<\/td>3<\/td>1<\/td>6561<\/td>54<\/td>0.00015241579027587<\/td>121.5<\/td>\n<\/tr>\n
9<\/td>6<\/td>5<\/td>2<\/td>1<\/td>59049<\/td>54<\/td>1.693508780843E-5<\/td>1093.5<\/td>\n<\/tr>\n
9<\/td>7<\/td>2<\/td>6<\/td>6<\/td>81<\/td>63<\/td>0.074074074074074<\/td>1.2857142857143<\/td>\n<\/tr>\n
9<\/td>7<\/td>3<\/td>5<\/td>3<\/td>729<\/td>63<\/td>0.0041152263374486<\/td>11.571428571429<\/td>\n<\/tr>\n
9<\/td>7<\/td>4<\/td>4<\/td>2<\/td>6561<\/td>63<\/td>0.00030483158055175<\/td>104.14285714286<\/td>\n<\/tr>\n
9<\/td>7<\/td>5<\/td>3<\/td>1<\/td>59049<\/td>63<\/td>1.693508780843E-5<\/td>937.28571428571<\/td>\n<\/tr>\n
9<\/td>7<\/td>6<\/td>2<\/td>1<\/td>531441<\/td>63<\/td>1.8816764231589E-6<\/td>8435.5714285714<\/td>\n<\/tr>\n
9<\/td>8<\/td>2<\/td>7<\/td>7<\/td>81<\/td>72<\/td>0.08641975308642<\/td>1.125<\/td>\n<\/tr>\n
9<\/td>8<\/td>3<\/td>6<\/td>3<\/td>729<\/td>72<\/td>0.0041152263374486<\/td>10.125<\/td>\n<\/tr>\n
9<\/td>8<\/td>4<\/td>5<\/td>2<\/td>6561<\/td>72<\/td>0.00030483158055175<\/td>91.125<\/td>\n<\/tr>\n
9<\/td>8<\/td>5<\/td>4<\/td>1<\/td>59049<\/td>72<\/td>1.693508780843E-5<\/td>820.125<\/td>\n<\/tr>\n
9<\/td>8<\/td>6<\/td>3<\/td>1<\/td>531441<\/td>72<\/td>1.8816764231589E-6<\/td>7381.125<\/td>\n<\/tr>\n
9<\/td>8<\/td>7<\/td>2<\/td>1<\/td>4782969<\/td>72<\/td>2.0907515812877E-7<\/td>66430.125<\/td>\n<\/tr>\n
9<\/td>9<\/td>2<\/td>8<\/td>8<\/td>81<\/td>81<\/td>0.098765432098765<\/td>1<\/td>\n<\/tr>\n
9<\/td>9<\/td>3<\/td>7<\/td>4<\/td>729<\/td>81<\/td>0.0054869684499314<\/td>9<\/td>\n<\/tr>\n
9<\/td>9<\/td>4<\/td>6<\/td>2<\/td>6561<\/td>81<\/td>0.00030483158055175<\/td>81<\/td>\n<\/tr>\n
9<\/td>9<\/td>5<\/td>5<\/td>2<\/td>59049<\/td>81<\/td>3.3870175616861E-5<\/td>729<\/td>\n<\/tr>\n
9<\/td>9<\/td>6<\/td>4<\/td>1<\/td>531441<\/td>81<\/td>1.8816764231589E-6<\/td>6561<\/td>\n<\/tr>\n
9<\/td>9<\/td>7<\/td>3<\/td>1<\/td>4782969<\/td>81<\/td>2.0907515812877E-7<\/td>59049<\/td>\n<\/tr>\n
9<\/td>9<\/td>8<\/td>2<\/td>1<\/td>43046721<\/td>81<\/td>2.3230573125419E-8<\/td>531441<\/td>\n<\/tr>\n
11<\/td>3<\/td>2<\/td>2<\/td>2<\/td>121<\/td>33<\/td>0.016528925619835<\/td>3.6666666666667<\/td>\n<\/tr>\n
11<\/td>4<\/td>2<\/td>3<\/td>3<\/td>121<\/td>44<\/td>0.024793388429752<\/td>2.75<\/td>\n<\/tr>\n
11<\/td>4<\/td>3<\/td>2<\/td>1<\/td>1331<\/td>44<\/td>0.00075131480090158<\/td>30.25<\/td>\n<\/tr>\n
11<\/td>5<\/td>2<\/td>4<\/td>4<\/td>121<\/td>55<\/td>0.033057851239669<\/td>2.2<\/td>\n<\/tr>\n
11<\/td>5<\/td>3<\/td>3<\/td>2<\/td>1331<\/td>55<\/td>0.0015026296018032<\/td>24.2<\/td>\n<\/tr>\n
11<\/td>5<\/td>4<\/td>2<\/td>1<\/td>14641<\/td>55<\/td>6.8301345536507E-5<\/td>266.2<\/td>\n<\/tr>\n
11<\/td>6<\/td>2<\/td>5<\/td>5<\/td>121<\/td>66<\/td>0.041322314049587<\/td>1.8333333333333<\/td>\n<\/tr>\n
11<\/td>6<\/td>3<\/td>4<\/td>2<\/td>1331<\/td>66<\/td>0.0015026296018032<\/td>20.166666666667<\/td>\n<\/tr>\n
11<\/td>6<\/td>4<\/td>3<\/td>1<\/td>14641<\/td>66<\/td>6.8301345536507E-5<\/td>221.83333333333<\/td>\n<\/tr>\n
11<\/td>6<\/td>5<\/td>2<\/td>1<\/td>161051<\/td>66<\/td>6.2092132305916E-6<\/td>2440.1666666667<\/td>\n<\/tr>\n
11<\/td>7<\/td>2<\/td>6<\/td>6<\/td>121<\/td>77<\/td>0.049586776859504<\/td>1.5714285714286<\/td>\n<\/tr>\n
11<\/td>7<\/td>3<\/td>5<\/td>3<\/td>1331<\/td>77<\/td>0.0022539444027047<\/td>17.285714285714<\/td>\n<\/tr>\n
11<\/td>7<\/td>4<\/td>4<\/td>2<\/td>14641<\/td>77<\/td>0.00013660269107301<\/td>190.14285714286<\/td>\n<\/tr>\n
11<\/td>7<\/td>5<\/td>3<\/td>1<\/td>161051<\/td>77<\/td>6.2092132305916E-6<\/td>2091.5714285714<\/td>\n<\/tr>\n
11<\/td>7<\/td>6<\/td>2<\/td>1<\/td>1771561<\/td>77<\/td>5.6447393005378E-7<\/td>23007.285714286<\/td>\n<\/tr>\n
11<\/td>8<\/td>2<\/td>7<\/td>7<\/td>121<\/td>88<\/td>0.057851239669421<\/td>1.375<\/td>\n<\/tr>\n
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19<\/td>19<\/td>8<\/td>12<\/td>2<\/td>16983563041<\/td>361<\/td>1.1776091949444E-10<\/td>47045881<\/td>\n<\/tr>\n
19<\/td>19<\/td>9<\/td>11<\/td>2<\/td>322687697779<\/td>361<\/td>6.1979431312865E-12<\/td>893871739<\/td>\n<\/tr>\n
19<\/td>19<\/td>10<\/td>10<\/td>2<\/td>6131066257801<\/td>361<\/td>3.262075332256E-13<\/td>16983563041<\/td>\n<\/tr>\n
19<\/td>19<\/td>11<\/td>9<\/td>1<\/td>116490258898219<\/td>361<\/td>8.5844087690948E-15<\/td>322687697779<\/td>\n<\/tr>\n
19<\/td>19<\/td>12<\/td>8<\/td>1<\/td>2213314919066161<\/td>361<\/td>4.518109878471E-16<\/td>6131066257801<\/td>\n<\/tr>\n
19<\/td>19<\/td>13<\/td>7<\/td>1<\/td>42052983462257056<\/td>361<\/td>2.3779525676163E-17<\/td>1.1649025889822E+14<\/td>\n<\/tr>\n
19<\/td>19<\/td>14<\/td>6<\/td>1<\/td>799006685782884096<\/td>361<\/td>1.2515539829559E-18<\/td>2213314919066161<\/td>\n<\/tr>\n
19<\/td>19<\/td>15<\/td>5<\/td>1<\/td>1.5181127029875E+19<\/td>361<\/td>6.5871262260839E-20<\/td>42052983462257056<\/td>\n<\/tr>\n
19<\/td>19<\/td>16<\/td>4<\/td>1<\/td>2.8844141356762E+20<\/td>361<\/td>3.4669085400442E-21<\/td>799006685782884096<\/td>\n<\/tr>\n
19<\/td>19<\/td>17<\/td>3<\/td>1<\/td>5.4803868577848E+21<\/td>361<\/td>1.8246887052864E-22<\/td>1.5181127029875E+19<\/td>\n<\/tr>\n
19<\/td>19<\/td>18<\/td>2<\/td>1<\/td>1.0412735029791E+23<\/td>361<\/td>9.6036247646653E-24<\/td>2.8844141356762E+20<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n

Each row of this table contains the parameters of a Reed-Solomon error-correcting code, and for each, the corresponding matrix size for the binary Kautz-Singleton image of the code as a group testing matrix. <\/p>\n\n\n\n

The columns represent:
q=code alphabet size (powers of primes)
n=codeword length (n <= q)
k=code dimension (k<n)
d=minimum Hamming distance of the code
D’=disjunct value of the binary group testing matrix (number of positives guaranteed to be detected)
N’=number of total people or samples in the group testing scheme
t=number of tests
D’\/N’ = guaranteed positivity (as a fraction)
N’\/t = samples\/tests (savings factor from using the group testing)<\/p>\n\n\n\n

References: <\/strong><\/p>\n\n\n\n

https:\/\/ieeexplore.ieee.org\/abstract\/document\/1053689?casa_token=89daZeyEQPgAAAAA:m9JVhaJyWxtNXzg88FekWWK7g1gQNBWlEN0OVcyDXGH9y3SLl_ZqrtJ12YC5UpOdwLNOzCY5<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Each row of this table contains the parameters of a Reed-Solomon error-correcting code, and for each, the corresponding matrix size for the binary Kautz-Singleton image of the code as a group testing matrix. The columns represent:q=code alphabet size (powers of primes)n=codeword length (n <= q)k=code dimension (k<n)d=minimum Hamming distance of the codeD’=disjunct value of the […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":125,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"page-templates\/full-width.php","meta":{"footnotes":""},"class_list":["post-227","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/khaymake.clasit.org\/index.php?rest_route=\/wp\/v2\/pages\/227","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/khaymake.clasit.org\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/khaymake.clasit.org\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/khaymake.clasit.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/khaymake.clasit.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=227"}],"version-history":[{"count":3,"href":"https:\/\/khaymake.clasit.org\/index.php?rest_route=\/wp\/v2\/pages\/227\/revisions"}],"predecessor-version":[{"id":235,"href":"https:\/\/khaymake.clasit.org\/index.php?rest_route=\/wp\/v2\/pages\/227\/revisions\/235"}],"up":[{"embeddable":true,"href":"https:\/\/khaymake.clasit.org\/index.php?rest_route=\/wp\/v2\/pages\/125"}],"wp:attachment":[{"href":"https:\/\/khaymake.clasit.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=227"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}