Information on Result #628071
Linear OA(510, 52, F5, 5) (dual of [52, 42, 6]-code), using trace code based on linear OA(255, 26, F25, 5) (dual of [26, 21, 6]-code or 26-arc in PG(4,25)), using
- extended Reed–Solomon code RSe(21,25) [i]
- the expurgated narrow-sense BCH-code C(I) with length 26 | 252−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- algebraic-geometric code AG(F,10P) with degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using the rational function field F25(x) [i]
- algebraic-geometric code AG(F, Q+6P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(5139, 390668, F5, 21) (dual of [390668, 390529, 22]-code) | [i] | Construction X with Cyclic Codes | |
| 2 | Linear OA(5137, 78164, F5, 23) (dual of [78164, 78027, 24]-code) | [i] | ||
| 3 | Linear OA(5123, 78164, F5, 21) (dual of [78164, 78041, 22]-code) | [i] | ||
| 4 | Linear OA(5119, 15660, F5, 23) (dual of [15660, 15541, 24]-code) | [i] | ||
| 5 | Linear OA(5107, 15660, F5, 21) (dual of [15660, 15553, 22]-code) | [i] | ||
| 6 | Linear OA(5143, 15672, F5, 27) (dual of [15672, 15529, 28]-code) | [i] | ||
| 7 | Linear OA(5141, 3156, F5, 33) (dual of [3156, 3015, 34]-code) | [i] | ||
| 8 | Linear OA(5131, 3156, F5, 31) (dual of [3156, 3025, 32]-code) | [i] | ||
| 9 | Linear OA(5101, 3156, F5, 23) (dual of [3156, 3055, 24]-code) | [i] | ||
| 10 | Linear OA(591, 3156, F5, 21) (dual of [3156, 3065, 22]-code) | [i] | ||
| 11 | Linear OA(5131, 3166, F5, 29) (dual of [3166, 3035, 30]-code) | [i] | ||
| 12 | Linear OA(5121, 3166, F5, 27) (dual of [3166, 3045, 28]-code) | [i] | ||
| 13 | Linear OA(5139, 660, F5, 39) (dual of [660, 521, 40]-code) | [i] | ||
| 14 | Linear OA(5131, 660, F5, 37) (dual of [660, 529, 38]-code) | [i] | ||
| 15 | Linear OA(5107, 660, F5, 29) (dual of [660, 553, 30]-code) | [i] | ||
| 16 | Linear OA(599, 660, F5, 27) (dual of [660, 561, 28]-code) | [i] | ||
| 17 | Linear OA(572, 663, F5, 19) (dual of [663, 591, 20]-code) | [i] | Construction XX with Cyclic Codes | |
| 18 | Linear OA(583, 670, F5, 22) (dual of [670, 587, 23]-code) | [i] | ||
| 19 | Linear OA(587, 670, F5, 23) (dual of [670, 583, 24]-code) | [i] | ||
| 20 | Linear OA(588, 663, F5, 24) (dual of [663, 575, 25]-code) | [i] | ||
| 21 | Linear OA(594, 669, F5, 25) (dual of [669, 575, 26]-code) | [i] | ||
| 22 | Linear OA(595, 671, F5, 25) (dual of [671, 576, 26]-code) | [i] | ||
| 23 | Linear OA(599, 670, F5, 27) (dual of [670, 571, 28]-code) | [i] | ||
| 24 | Linear OA(5103, 670, F5, 28) (dual of [670, 567, 29]-code) | [i] | ||
| 25 | Linear OA(5123, 680, F5, 33) (dual of [680, 557, 34]-code) | [i] | ||
| 26 | Linear OA(5122, 663, F5, 35) (dual of [663, 541, 36]-code) | [i] | ||
| 27 | Linear OA(5139, 690, F5, 37) (dual of [690, 551, 38]-code) | [i] | ||
| 28 | Linear OA(5143, 690, F5, 38) (dual of [690, 547, 39]-code) | [i] | ||
| 29 | Linear OA(5141, 684, F5, 38) (dual of [684, 543, 39]-code) | [i] | ||
| 30 | Linear OA(5131, 674, F5, 37) (dual of [674, 543, 38]-code) | [i] | ||
| 31 | Linear OA(5129, 670, F5, 37) (dual of [670, 541, 38]-code) | [i] | ||
| 32 | Linear OA(5136, 677, F5, 38) (dual of [677, 541, 39]-code) | [i] | ||
| 33 | Linear OA(5133, 670, F5, 38) (dual of [670, 537, 39]-code) | [i] | ||
| 34 | Linear OA(5143, 684, F5, 39) (dual of [684, 541, 40]-code) | [i] | ||
| 35 | Linear OA(5143, 684, F5, 39) (dual of [684, 541, 40]-code) | [i] | ||
| 36 | Linear OA(5148, 685, F5, 40) (dual of [685, 537, 41]-code) | [i] | ||
| 37 | Linear OA(5147, 682, F5, 40) (dual of [682, 535, 41]-code) | [i] | ||
| 38 | Linear OA(5140, 677, F5, 39) (dual of [677, 537, 40]-code) | [i] | ||
| 39 | Linear OA(5134, 663, F5, 39) (dual of [663, 529, 40]-code) | [i] | ||
| 40 | Linear OA(5147, 684, F5, 40) (dual of [684, 537, 41]-code) | [i] | ||
| 41 | Linear OA(5147, 684, F5, 40) (dual of [684, 537, 41]-code) | [i] | ||
| 42 | Linear OA(5144, 677, F5, 40) (dual of [677, 533, 41]-code) | [i] | ||
| 43 | Linear OA(5140, 669, F5, 40) (dual of [669, 529, 41]-code) | [i] | ||
| 44 | Linear OA(5141, 671, F5, 40) (dual of [671, 530, 41]-code) | [i] | ||
| 45 | Linear OA(5148, 677, F5, 42) (dual of [677, 529, 43]-code) | [i] | ||
| 46 | Linear OA(5145, 670, F5, 42) (dual of [670, 525, 43]-code) | [i] | ||
| 47 | Linear OA(5149, 670, F5, 43) (dual of [670, 521, 44]-code) | [i] | ||
| 48 | Linear OA(5150, 663, F5, 44) (dual of [663, 513, 45]-code) | [i] | ||
| 49 | Linear OA(5146, 1953177, F5, 19) (dual of [1953177, 1953031, 20]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 50 | Linear OA(5137, 1953177, F5, 18) (dual of [1953177, 1953040, 19]-code) | [i] | ||
| 51 | Linear OA(5128, 1953177, F5, 17) (dual of [1953177, 1953049, 18]-code) | [i] | ||
| 52 | Linear OA(5119, 1953177, F5, 15) (dual of [1953177, 1953058, 16]-code) | [i] | ||
| 53 | Linear OA(5110, 1953177, F5, 14) (dual of [1953177, 1953067, 15]-code) | [i] | ||
| 54 | Linear OA(5147, 390675, F5, 22) (dual of [390675, 390528, 23]-code) | [i] | ||
| 55 | Linear OA(5139, 390675, F5, 20) (dual of [390675, 390536, 21]-code) | [i] | ||
| 56 | Linear OA(5131, 390675, F5, 19) (dual of [390675, 390544, 20]-code) | [i] | ||
| 57 | Linear OA(5123, 390675, F5, 18) (dual of [390675, 390552, 19]-code) | [i] | ||
| 58 | Linear OA(5115, 390675, F5, 17) (dual of [390675, 390560, 18]-code) | [i] | ||
| 59 | Linear OA(5107, 390675, F5, 15) (dual of [390675, 390568, 16]-code) | [i] | ||
| 60 | Linear OA(599, 390675, F5, 14) (dual of [390675, 390576, 15]-code) | [i] | ||
| 61 | Linear OA(5144, 78170, F5, 24) (dual of [78170, 78026, 25]-code) | [i] | ||
| 62 | Linear OA(5137, 78170, F5, 23) (dual of [78170, 78033, 24]-code) | [i] | ||
| 63 | Linear OA(5130, 78170, F5, 22) (dual of [78170, 78040, 23]-code) | [i] | ||
| 64 | Linear OA(5123, 78170, F5, 20) (dual of [78170, 78047, 21]-code) | [i] | ||
| 65 | Linear OA(5116, 78170, F5, 19) (dual of [78170, 78054, 20]-code) | [i] | ||
| 66 | Linear OA(5109, 78170, F5, 18) (dual of [78170, 78061, 19]-code) | [i] | ||
| 67 | Linear OA(5102, 78170, F5, 17) (dual of [78170, 78068, 18]-code) | [i] | ||
| 68 | Linear OA(595, 78170, F5, 15) (dual of [78170, 78075, 16]-code) | [i] | ||
| 69 | Linear OA(588, 78170, F5, 14) (dual of [78170, 78082, 15]-code) | [i] | ||
| 70 | Linear OA(5149, 15665, F5, 29) (dual of [15665, 15516, 30]-code) | [i] | ||
| 71 | Linear OA(5143, 15665, F5, 28) (dual of [15665, 15522, 29]-code) | [i] | ||
| 72 | Linear OA(5137, 15665, F5, 27) (dual of [15665, 15528, 28]-code) | [i] | ||
| 73 | Linear OA(5131, 15665, F5, 25) (dual of [15665, 15534, 26]-code) | [i] | ||
| 74 | Linear OA(5125, 15665, F5, 24) (dual of [15665, 15540, 25]-code) | [i] | ||
| 75 | Linear OA(5119, 15665, F5, 23) (dual of [15665, 15546, 24]-code) | [i] | ||
| 76 | Linear OA(5113, 15665, F5, 22) (dual of [15665, 15552, 23]-code) | [i] | ||
| 77 | Linear OA(5107, 15665, F5, 20) (dual of [15665, 15558, 21]-code) | [i] | ||
| 78 | Linear OA(5101, 15665, F5, 19) (dual of [15665, 15564, 20]-code) | [i] | ||
| 79 | Linear OA(595, 15665, F5, 18) (dual of [15665, 15570, 19]-code) | [i] | ||
| 80 | Linear OA(589, 15665, F5, 17) (dual of [15665, 15576, 18]-code) | [i] | ||
| 81 | Linear OA(583, 15665, F5, 15) (dual of [15665, 15582, 16]-code) | [i] | ||
| 82 | Linear OA(577, 15665, F5, 14) (dual of [15665, 15588, 15]-code) | [i] | ||
| 83 | Linear OA(5146, 3160, F5, 34) (dual of [3160, 3014, 35]-code) | [i] | ||
| 84 | Linear OA(5141, 3160, F5, 33) (dual of [3160, 3019, 34]-code) | [i] | ||
| 85 | Linear OA(5136, 3160, F5, 32) (dual of [3160, 3024, 33]-code) | [i] | ||
| 86 | Linear OA(5131, 3160, F5, 30) (dual of [3160, 3029, 31]-code) | [i] | ||
| 87 | Linear OA(5126, 3160, F5, 29) (dual of [3160, 3034, 30]-code) | [i] | ||
| 88 | Linear OA(5121, 3160, F5, 28) (dual of [3160, 3039, 29]-code) | [i] | ||
| 89 | Linear OA(5116, 3160, F5, 27) (dual of [3160, 3044, 28]-code) | [i] | ||
| 90 | Linear OA(5111, 3160, F5, 25) (dual of [3160, 3049, 26]-code) | [i] | ||
| 91 | Linear OA(5106, 3160, F5, 24) (dual of [3160, 3054, 25]-code) | [i] | ||
| 92 | Linear OA(5101, 3160, F5, 23) (dual of [3160, 3059, 24]-code) | [i] | ||
| 93 | Linear OA(596, 3160, F5, 22) (dual of [3160, 3064, 23]-code) | [i] | ||
| 94 | Linear OA(591, 3160, F5, 20) (dual of [3160, 3069, 21]-code) | [i] | ||
| 95 | Linear OA(586, 3160, F5, 19) (dual of [3160, 3074, 20]-code) | [i] | ||
| 96 | Linear OA(581, 3160, F5, 18) (dual of [3160, 3079, 19]-code) | [i] | ||
| 97 | Linear OA(576, 3160, F5, 17) (dual of [3160, 3084, 18]-code) | [i] | ||
| 98 | Linear OA(5149, 655, F5, 44) (dual of [655, 506, 45]-code) | [i] | ||
| 99 | Linear OA(5145, 655, F5, 43) (dual of [655, 510, 44]-code) | [i] | ||
| 100 | Linear OA(5141, 655, F5, 42) (dual of [655, 514, 43]-code) | [i] | ||
| 101 | Linear OA(5137, 655, F5, 40) (dual of [655, 518, 41]-code) | [i] | ||
| 102 | Linear OA(5133, 655, F5, 39) (dual of [655, 522, 40]-code) | [i] | ||
| 103 | Linear OA(5129, 655, F5, 38) (dual of [655, 526, 39]-code) | [i] | ||
| 104 | Linear OA(5125, 655, F5, 37) (dual of [655, 530, 38]-code) | [i] | ||
| 105 | Linear OA(5121, 655, F5, 35) (dual of [655, 534, 36]-code) | [i] | ||
| 106 | Linear OA(5117, 655, F5, 34) (dual of [655, 538, 35]-code) | [i] | ||
| 107 | Linear OA(5113, 655, F5, 33) (dual of [655, 542, 34]-code) | [i] | ||
| 108 | Linear OA(587, 655, F5, 24) (dual of [655, 568, 25]-code) | [i] | ||
| 109 | Linear OA(583, 655, F5, 23) (dual of [655, 572, 24]-code) | [i] | ||
| 110 | Linear OA(579, 655, F5, 22) (dual of [655, 576, 23]-code) | [i] | ||
| 111 | Linear OA(575, 655, F5, 20) (dual of [655, 580, 21]-code) | [i] | ||
| 112 | Linear OA(571, 655, F5, 19) (dual of [655, 584, 20]-code) | [i] | ||
| 113 | Linear OA(567, 655, F5, 18) (dual of [655, 588, 19]-code) | [i] | ||
| 114 | Linear OA(563, 655, F5, 17) (dual of [655, 592, 18]-code) | [i] | ||
| 115 | Linear OA(5150, 657, F5, 44) (dual of [657, 507, 45]-code) | [i] | Construction XX with a Chain of Extended Narrow-Sense BCH Codes | |
| 116 | Linear OA(5146, 657, F5, 43) (dual of [657, 511, 44]-code) | [i] | ||
| 117 | Linear OA(5144, 660, F5, 42) (dual of [660, 516, 43]-code) | [i] | ||
| 118 | Linear OA(5143, 658, F5, 42) (dual of [658, 515, 43]-code) | [i] | ||
| 119 | Linear OA(5138, 657, F5, 40) (dual of [657, 519, 41]-code) | [i] | ||
| 120 | Linear OA(5134, 657, F5, 39) (dual of [657, 523, 40]-code) | [i] | ||
| 121 | Linear OA(5130, 657, F5, 38) (dual of [657, 527, 39]-code) | [i] | ||
| 122 | Linear OA(5128, 660, F5, 37) (dual of [660, 532, 38]-code) | [i] | ||
| 123 | Linear OA(5127, 658, F5, 37) (dual of [658, 531, 38]-code) | [i] | ||
| 124 | Linear OA(5122, 657, F5, 35) (dual of [657, 535, 36]-code) | [i] | ||
| 125 | Linear OA(5118, 657, F5, 34) (dual of [657, 539, 35]-code) | [i] | ||
| 126 | Linear OA(5114, 657, F5, 33) (dual of [657, 543, 34]-code) | [i] | ||
| 127 | Linear OA(5118, 663, F5, 33) (dual of [663, 545, 34]-code) | [i] | ||
| 128 | Linear OA(5112, 658, F5, 32) (dual of [658, 546, 33]-code) | [i] | ||
| 129 | Linear OA(5106, 655, F5, 30) (dual of [655, 549, 31]-code) | [i] | ||
| 130 | Linear OA(5102, 655, F5, 29) (dual of [655, 553, 30]-code) | [i] | ||
| 131 | Linear OA(598, 655, F5, 28) (dual of [655, 557, 29]-code) | [i] | ||
| 132 | Linear OA(596, 658, F5, 27) (dual of [658, 562, 28]-code) | [i] | ||
| 133 | Linear OA(595, 656, F5, 27) (dual of [656, 561, 28]-code) | [i] | ||
| 134 | Linear OA(592, 657, F5, 25) (dual of [657, 565, 26]-code) | [i] | ||
| 135 | Linear OA(588, 657, F5, 24) (dual of [657, 569, 25]-code) | [i] | ||
| 136 | Linear OA(584, 657, F5, 23) (dual of [657, 573, 24]-code) | [i] | ||
| 137 | Linear OA(582, 660, F5, 22) (dual of [660, 578, 23]-code) | [i] | ||
| 138 | Linear OA(581, 658, F5, 22) (dual of [658, 577, 23]-code) | [i] | ||
| 139 | Linear OA(576, 657, F5, 20) (dual of [657, 581, 21]-code) | [i] | ||
| 140 | Linear OA(572, 657, F5, 19) (dual of [657, 585, 20]-code) | [i] | ||
| 141 | Linear OA(568, 657, F5, 18) (dual of [657, 589, 19]-code) | [i] | ||