Information on Result #628075
Linear OA(514, 52, F5, 7) (dual of [52, 38, 8]-code), using trace code based on linear OA(257, 26, F25, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using
- extended Reed–Solomon code RSe(19,25) [i]
- the expurgated narrow-sense BCH-code C(I) with length 26 | 252−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- algebraic-geometric code AG(F,9P) 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,6P) with 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(5143, 390678, F5, 21) (dual of [390678, 390535, 22]-code) | [i] | Construction X with Cyclic Codes | |
| 2 | Linear OA(5141, 78178, F5, 23) (dual of [78178, 78037, 24]-code) | [i] | ||
| 3 | Linear OA(5127, 78178, F5, 21) (dual of [78178, 78051, 22]-code) | [i] | ||
| 4 | Linear OA(5135, 15676, F5, 25) (dual of [15676, 15541, 26]-code) | [i] | ||
| 5 | Linear OA(5123, 15676, F5, 23) (dual of [15676, 15553, 24]-code) | [i] | ||
| 6 | Linear OA(5111, 15676, F5, 21) (dual of [15676, 15565, 22]-code) | [i] | ||
| 7 | Linear OA(5145, 3170, F5, 33) (dual of [3170, 3025, 34]-code) | [i] | ||
| 8 | Linear OA(5135, 3170, F5, 31) (dual of [3170, 3035, 32]-code) | [i] | ||
| 9 | Linear OA(5115, 3170, F5, 25) (dual of [3170, 3055, 26]-code) | [i] | ||
| 10 | Linear OA(5105, 3170, F5, 23) (dual of [3170, 3065, 24]-code) | [i] | ||
| 11 | Linear OA(595, 3170, F5, 21) (dual of [3170, 3075, 22]-code) | [i] | ||
| 12 | Linear OA(5135, 3178, F5, 29) (dual of [3178, 3043, 30]-code) | [i] | ||
| 13 | Linear OA(5143, 664, F5, 41) (dual of [664, 521, 42]-code) | [i] | ||
| 14 | Linear OA(5127, 664, F5, 35) (dual of [664, 537, 36]-code) | [i] | ||
| 15 | Linear OA(5119, 664, F5, 33) (dual of [664, 545, 34]-code) | [i] | ||
| 16 | Linear OA(5111, 664, F5, 31) (dual of [664, 553, 32]-code) | [i] | ||
| 17 | Linear OA(595, 664, F5, 25) (dual of [664, 569, 26]-code) | [i] | ||
| 18 | Linear OA(587, 664, F5, 23) (dual of [664, 577, 24]-code) | [i] | ||
| 19 | Linear OA(579, 664, F5, 21) (dual of [664, 585, 22]-code) | [i] | ||
| 20 | Linear OA(5143, 672, F5, 39) (dual of [672, 529, 40]-code) | [i] | ||
| 21 | Linear OA(584, 666, F5, 22) (dual of [666, 582, 23]-code) | [i] | Construction XX with Cyclic Codes | |
| 22 | Linear OA(583, 664, F5, 22) (dual of [664, 581, 23]-code) | [i] | ||
| 23 | Linear OA(588, 666, F5, 23) (dual of [666, 578, 24]-code) | [i] | ||
| 24 | Linear OA(588, 669, F5, 23) (dual of [669, 581, 24]-code) | [i] | ||
| 25 | Linear OA(5102, 666, F5, 28) (dual of [666, 564, 29]-code) | [i] | ||
| 26 | Linear OA(5101, 664, F5, 28) (dual of [664, 563, 29]-code) | [i] | ||
| 27 | Linear OA(5106, 669, F5, 29) (dual of [669, 563, 30]-code) | [i] | ||
| 28 | Linear OA(5114, 666, F5, 32) (dual of [666, 552, 33]-code) | [i] | ||
| 29 | Linear OA(5113, 664, F5, 32) (dual of [664, 551, 33]-code) | [i] | ||
| 30 | Linear OA(5117, 676, F5, 32) (dual of [676, 559, 33]-code) | [i] | ||
| 31 | Linear OA(5118, 666, F5, 33) (dual of [666, 548, 34]-code) | [i] | ||
| 32 | Linear OA(5117, 664, F5, 33) (dual of [664, 547, 34]-code) | [i] | ||
| 33 | Linear OA(5120, 672, F5, 33) (dual of [672, 552, 34]-code) | [i] | ||
| 34 | Linear OA(5118, 669, F5, 33) (dual of [669, 551, 34]-code) | [i] | ||
| 35 | Linear OA(5121, 676, F5, 33) (dual of [676, 555, 34]-code) | [i] | ||
| 36 | Linear OA(5127, 680, F5, 34) (dual of [680, 553, 35]-code) | [i] | ||
| 37 | Linear OA(5124, 672, F5, 34) (dual of [672, 548, 35]-code) | [i] | ||
| 38 | Linear OA(5122, 669, F5, 34) (dual of [669, 547, 35]-code) | [i] | ||
| 39 | Linear OA(5125, 677, F5, 34) (dual of [677, 552, 35]-code) | [i] | ||
| 40 | Linear OA(5124, 675, F5, 34) (dual of [675, 551, 35]-code) | [i] | ||
| 41 | Linear OA(5131, 680, F5, 35) (dual of [680, 549, 36]-code) | [i] | ||
| 42 | Linear OA(5129, 674, F5, 35) (dual of [674, 545, 36]-code) | [i] | ||
| 43 | Linear OA(5129, 677, F5, 35) (dual of [677, 548, 36]-code) | [i] | ||
| 44 | Linear OA(5128, 675, F5, 35) (dual of [675, 547, 36]-code) | [i] | ||
| 45 | Linear OA(5134, 686, F5, 36) (dual of [686, 552, 37]-code) | [i] | ||
| 46 | Linear OA(5132, 683, F5, 36) (dual of [683, 551, 37]-code) | [i] | ||
| 47 | Linear OA(5129, 680, F5, 35) (dual of [680, 551, 36]-code) | [i] | ||
| 48 | Linear OA(5129, 676, F5, 36) (dual of [676, 547, 37]-code) | [i] | ||
| 49 | Linear OA(5130, 666, F5, 37) (dual of [666, 536, 38]-code) | [i] | ||
| 50 | Linear OA(5129, 664, F5, 37) (dual of [664, 535, 38]-code) | [i] | ||
| 51 | Linear OA(5138, 687, F5, 37) (dual of [687, 549, 38]-code) | [i] | ||
| 52 | Linear OA(5135, 680, F5, 37) (dual of [680, 545, 38]-code) | [i] | ||
| 53 | Linear OA(5136, 683, F5, 37) (dual of [683, 547, 38]-code) | [i] | ||
| 54 | Linear OA(5133, 676, F5, 37) (dual of [676, 543, 38]-code) | [i] | ||
| 55 | Linear OA(5139, 690, F5, 37) (dual of [690, 551, 38]-code) | [i] | ||
| 56 | Linear OA(5143, 688, F5, 38) (dual of [688, 545, 39]-code) | [i] | ||
| 57 | Linear OA(5139, 680, F5, 38) (dual of [680, 541, 39]-code) | [i] | ||
| 58 | Linear OA(5137, 676, F5, 38) (dual of [676, 539, 39]-code) | [i] | ||
| 59 | Linear OA(5134, 666, F5, 38) (dual of [666, 532, 39]-code) | [i] | ||
| 60 | Linear OA(5133, 664, F5, 38) (dual of [664, 531, 39]-code) | [i] | ||
| 61 | Linear OA(5142, 687, F5, 38) (dual of [687, 545, 39]-code) | [i] | ||
| 62 | Linear OA(5134, 669, F5, 38) (dual of [669, 535, 39]-code) | [i] | ||
| 63 | Linear OA(5143, 690, F5, 38) (dual of [690, 547, 39]-code) | [i] | ||
| 64 | Linear OA(5140, 683, F5, 38) (dual of [683, 543, 39]-code) | [i] | ||
| 65 | Linear OA(5143, 680, F5, 39) (dual of [680, 537, 40]-code) | [i] | ||
| 66 | Linear OA(5141, 676, F5, 39) (dual of [676, 535, 40]-code) | [i] | ||
| 67 | Linear OA(5140, 671, F5, 39) (dual of [671, 531, 40]-code) | [i] | ||
| 68 | Linear OA(5144, 683, F5, 39) (dual of [683, 539, 40]-code) | [i] | ||
| 69 | Linear OA(5140, 673, F5, 39) (dual of [673, 533, 40]-code) | [i] | ||
| 70 | Linear OA(5138, 669, F5, 39) (dual of [669, 531, 40]-code) | [i] | ||
| 71 | Linear OA(5141, 677, F5, 39) (dual of [677, 536, 40]-code) | [i] | ||
| 72 | Linear OA(5140, 675, F5, 39) (dual of [675, 535, 40]-code) | [i] | ||
| 73 | Linear OA(5148, 683, F5, 40) (dual of [683, 535, 41]-code) | [i] | ||
| 74 | Linear OA(5145, 676, F5, 40) (dual of [676, 531, 41]-code) | [i] | ||
| 75 | Linear OA(5142, 669, F5, 40) (dual of [669, 527, 41]-code) | [i] | ||
| 76 | Linear OA(5147, 680, F5, 40) (dual of [680, 533, 41]-code) | [i] | ||
| 77 | Linear OA(5145, 677, F5, 40) (dual of [677, 532, 41]-code) | [i] | ||
| 78 | Linear OA(5144, 675, F5, 40) (dual of [675, 531, 41]-code) | [i] | ||
| 79 | Linear OA(5147, 680, F5, 41) (dual of [680, 533, 42]-code) | [i] | ||
| 80 | Linear OA(5145, 676, F5, 41) (dual of [676, 531, 42]-code) | [i] | ||
| 81 | Linear OA(5148, 683, F5, 41) (dual of [683, 535, 42]-code) | [i] | ||
| 82 | Linear OA(5145, 680, F5, 40) (dual of [680, 535, 41]-code) | [i] | ||
| 83 | Linear OA(5146, 666, F5, 42) (dual of [666, 520, 43]-code) | [i] | ||
| 84 | Linear OA(5145, 664, F5, 42) (dual of [664, 519, 43]-code) | [i] | ||
| 85 | Linear OA(5149, 676, F5, 42) (dual of [676, 527, 43]-code) | [i] | ||
| 86 | Linear OA(5150, 666, F5, 43) (dual of [666, 516, 44]-code) | [i] | ||
| 87 | Linear OA(5149, 664, F5, 43) (dual of [664, 515, 44]-code) | [i] | ||
| 88 | Linear OA(5150, 669, F5, 43) (dual of [669, 519, 44]-code) | [i] | ||
| 89 | Linear OA(5134, 78177, F5, 22) (dual of [78177, 78043, 23]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 90 | Linear OA(5141, 15675, F5, 27) (dual of [15675, 15534, 28]-code) | [i] | ||
| 91 | Linear OA(5135, 15675, F5, 26) (dual of [15675, 15540, 27]-code) | [i] | ||
| 92 | Linear OA(5117, 15675, F5, 22) (dual of [15675, 15558, 23]-code) | [i] | ||
| 93 | Linear OA(5135, 15677, F5, 25) (dual of [15677, 15542, 26]-code) | [i] | ||
| 94 | Linear OA(5129, 15677, F5, 24) (dual of [15677, 15548, 25]-code) | [i] | ||
| 95 | Linear OA(5111, 15677, F5, 20) (dual of [15677, 15566, 21]-code) | [i] | ||
| 96 | Linear OA(5105, 15677, F5, 19) (dual of [15677, 15572, 20]-code) | [i] | ||
| 97 | Linear OA(5140, 3169, F5, 32) (dual of [3169, 3029, 33]-code) | [i] | ||
| 98 | Linear OA(5120, 3169, F5, 27) (dual of [3169, 3049, 28]-code) | [i] | ||
| 99 | Linear OA(5115, 3169, F5, 26) (dual of [3169, 3054, 27]-code) | [i] | ||
| 100 | Linear OA(5100, 3169, F5, 22) (dual of [3169, 3069, 23]-code) | [i] | ||
| 101 | Linear OA(5150, 3174, F5, 34) (dual of [3174, 3024, 35]-code) | [i] | ||
| 102 | Linear OA(5135, 3174, F5, 30) (dual of [3174, 3039, 31]-code) | [i] | ||
| 103 | Linear OA(5130, 3174, F5, 29) (dual of [3174, 3044, 30]-code) | [i] | ||
| 104 | Linear OA(5115, 3174, F5, 25) (dual of [3174, 3059, 26]-code) | [i] | ||
| 105 | Linear OA(5110, 3174, F5, 24) (dual of [3174, 3064, 25]-code) | [i] | ||
| 106 | Linear OA(5145, 663, F5, 42) (dual of [663, 518, 43]-code) | [i] | ||
| 107 | Linear OA(5141, 663, F5, 41) (dual of [663, 522, 42]-code) | [i] | ||
| 108 | Linear OA(5129, 663, F5, 37) (dual of [663, 534, 38]-code) | [i] | ||
| 109 | Linear OA(5125, 663, F5, 36) (dual of [663, 538, 37]-code) | [i] | ||
| 110 | Linear OA(5113, 661, F5, 32) (dual of [661, 548, 33]-code) | [i] | ||
| 111 | Linear OA(5109, 661, F5, 31) (dual of [661, 552, 32]-code) | [i] | ||
| 112 | Linear OA(597, 661, F5, 27) (dual of [661, 564, 28]-code) | [i] | ||
| 113 | Linear OA(595, 663, F5, 26) (dual of [663, 568, 27]-code) | [i] | ||
| 114 | Linear OA(583, 663, F5, 22) (dual of [663, 580, 23]-code) | [i] | ||
| 115 | Linear OA(5141, 667, F5, 40) (dual of [667, 526, 41]-code) | [i] | ||
| 116 | Linear OA(5137, 667, F5, 39) (dual of [667, 530, 40]-code) | [i] | ||
| 117 | Linear OA(5125, 667, F5, 35) (dual of [667, 542, 36]-code) | [i] | ||
| 118 | Linear OA(5121, 665, F5, 34) (dual of [665, 544, 35]-code) | [i] | ||
| 119 | Linear OA(5109, 665, F5, 30) (dual of [665, 556, 31]-code) | [i] | ||
| 120 | Linear OA(5105, 665, F5, 29) (dual of [665, 560, 30]-code) | [i] | ||
| 121 | Linear OA(595, 667, F5, 25) (dual of [667, 572, 26]-code) | [i] | ||
| 122 | Linear OA(591, 667, F5, 24) (dual of [667, 576, 25]-code) | [i] | ||
| 123 | Linear OOA(514, 26, F5, 2, 7) (dual of [(26, 2), 38, 8]-NRT-code) | [i] | OOA Folding | |