Information on Result #684416
Linear OA(510, 28, F5, 6) (dual of [28, 18, 7]-code), using construction X applied to Ce(5) ⊂ Ce(3) based on
- linear OA(59, 25, F5, 6) (dual of [25, 16, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(57, 25, F5, 4) (dual of [25, 18, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(51, 3, F5, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
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(5105, 652, F5, 31) (dual of [652, 547, 32]-code) | [i] | Construction X with Cyclic Codes | |
| 2 | Linear OA(564, 657, F5, 17) (dual of [657, 593, 18]-code) | [i] | Construction XX with Cyclic Codes | |
| 3 | Linear OA(564, 658, F5, 17) (dual of [658, 594, 18]-code) | [i] | ||
| 4 | Linear OA(563, 656, F5, 17) (dual of [656, 593, 18]-code) | [i] | ||
| 5 | Linear OA(567, 656, F5, 18) (dual of [656, 589, 19]-code) | [i] | ||
| 6 | Linear OA(568, 661, F5, 18) (dual of [661, 593, 19]-code) | [i] | ||
| 7 | Linear OA(571, 656, F5, 19) (dual of [656, 585, 20]-code) | [i] | ||
| 8 | Linear OA(572, 661, F5, 19) (dual of [661, 589, 20]-code) | [i] | ||
| 9 | Linear OA(576, 661, F5, 20) (dual of [661, 585, 21]-code) | [i] | ||
| 10 | Linear OA(575, 656, F5, 20) (dual of [656, 581, 21]-code) | [i] | ||
| 11 | Linear OA(579, 668, F5, 21) (dual of [668, 589, 22]-code) | [i] | ||
| 12 | Linear OA(576, 657, F5, 21) (dual of [657, 581, 22]-code) | [i] | ||
| 13 | Linear OA(583, 668, F5, 22) (dual of [668, 585, 23]-code) | [i] | ||
| 14 | Linear OA(580, 657, F5, 22) (dual of [657, 577, 23]-code) | [i] | ||
| 15 | Linear OA(580, 658, F5, 22) (dual of [658, 578, 23]-code) | [i] | ||
| 16 | Linear OA(579, 656, F5, 22) (dual of [656, 577, 23]-code) | [i] | ||
| 17 | Linear OA(587, 668, F5, 23) (dual of [668, 581, 24]-code) | [i] | ||
| 18 | Linear OA(583, 656, F5, 23) (dual of [656, 573, 24]-code) | [i] | ||
| 19 | Linear OA(584, 661, F5, 23) (dual of [661, 577, 24]-code) | [i] | ||
| 20 | Linear OA(591, 668, F5, 24) (dual of [668, 577, 25]-code) | [i] | ||
| 21 | Linear OA(587, 656, F5, 24) (dual of [656, 569, 25]-code) | [i] | ||
| 22 | Linear OA(588, 661, F5, 24) (dual of [661, 573, 25]-code) | [i] | ||
| 23 | Linear OA(591, 669, F5, 24) (dual of [669, 578, 25]-code) | [i] | ||
| 24 | Linear OA(590, 667, F5, 24) (dual of [667, 577, 25]-code) | [i] | ||
| 25 | Linear OA(595, 668, F5, 25) (dual of [668, 573, 26]-code) | [i] | ||
| 26 | Linear OA(592, 661, F5, 25) (dual of [661, 569, 26]-code) | [i] | ||
| 27 | Linear OA(591, 656, F5, 25) (dual of [656, 565, 26]-code) | [i] | ||
| 28 | Linear OA(595, 672, F5, 25) (dual of [672, 577, 26]-code) | [i] | ||
| 29 | Linear OA(595, 668, F5, 26) (dual of [668, 573, 27]-code) | [i] | ||
| 30 | Linear OA(592, 657, F5, 26) (dual of [657, 565, 27]-code) | [i] | ||
| 31 | Linear OA(599, 668, F5, 27) (dual of [668, 569, 28]-code) | [i] | ||
| 32 | Linear OA(5103, 668, F5, 28) (dual of [668, 565, 29]-code) | [i] | ||
| 33 | Linear OA(5100, 661, F5, 28) (dual of [661, 561, 29]-code) | [i] | ||
| 34 | Linear OA(5101, 656, F5, 29) (dual of [656, 555, 30]-code) | [i] | ||
| 35 | Linear OA(5105, 656, F5, 30) (dual of [656, 551, 31]-code) | [i] | ||
| 36 | Linear OA(5106, 661, F5, 30) (dual of [661, 555, 31]-code) | [i] | ||
| 37 | Linear OA(5105, 653, F5, 31) (dual of [653, 548, 32]-code) | [i] | ||
| 38 | Linear OA(5114, 675, F5, 31) (dual of [675, 561, 32]-code) | [i] | ||
| 39 | Linear OA(5111, 672, F5, 30) (dual of [672, 561, 31]-code) | [i] | ||
| 40 | Linear OA(5111, 668, F5, 31) (dual of [668, 557, 32]-code) | [i] | ||
| 41 | Linear OA(5110, 658, F5, 32) (dual of [658, 548, 33]-code) | [i] | ||
| 42 | Linear OA(5109, 656, F5, 32) (dual of [656, 547, 33]-code) | [i] | ||
| 43 | Linear OA(5122, 679, F5, 33) (dual of [679, 557, 34]-code) | [i] | ||
| 44 | Linear OA(5119, 672, F5, 33) (dual of [672, 553, 34]-code) | [i] | ||
| 45 | Linear OA(5116, 664, F5, 33) (dual of [664, 548, 34]-code) | [i] | ||
| 46 | Linear OA(5114, 661, F5, 33) (dual of [661, 547, 34]-code) | [i] | ||
| 47 | Linear OA(5117, 668, F5, 33) (dual of [668, 551, 34]-code) | [i] | ||
| 48 | Linear OA(5126, 679, F5, 34) (dual of [679, 553, 35]-code) | [i] | ||
| 49 | Linear OA(5123, 672, F5, 34) (dual of [672, 549, 35]-code) | [i] | ||
| 50 | Linear OA(5121, 669, F5, 34) (dual of [669, 548, 35]-code) | [i] | ||
| 51 | Linear OA(5120, 667, F5, 34) (dual of [667, 547, 35]-code) | [i] | ||
| 52 | Linear OA(5118, 661, F5, 34) (dual of [661, 543, 35]-code) | [i] | ||
| 53 | Linear OA(5130, 679, F5, 35) (dual of [679, 549, 36]-code) | [i] | ||
| 54 | Linear OA(5127, 672, F5, 35) (dual of [672, 545, 36]-code) | [i] | ||
| 55 | Linear OA(5121, 656, F5, 35) (dual of [656, 535, 36]-code) | [i] | ||
| 56 | Linear OA(5122, 661, F5, 35) (dual of [661, 539, 36]-code) | [i] | ||
| 57 | Linear OA(5130, 678, F5, 36) (dual of [678, 548, 37]-code) | [i] | ||
| 58 | Linear OA(5128, 675, F5, 36) (dual of [675, 547, 37]-code) | [i] | ||
| 59 | Linear OA(5125, 672, F5, 35) (dual of [672, 547, 36]-code) | [i] | ||
| 60 | Linear OA(5125, 668, F5, 36) (dual of [668, 543, 37]-code) | [i] | ||
| 61 | Linear OA(5122, 657, F5, 36) (dual of [657, 535, 37]-code) | [i] | ||
| 62 | Linear OA(5137, 685, F5, 37) (dual of [685, 548, 38]-code) | [i] | ||
| 63 | Linear OA(5143, 688, F5, 38) (dual of [688, 545, 39]-code) | [i] | ||
| 64 | Linear OA(5131, 672, F5, 37) (dual of [672, 541, 38]-code) | [i] | ||
| 65 | Linear OA(5129, 668, F5, 37) (dual of [668, 539, 38]-code) | [i] | ||
| 66 | Linear OA(5126, 657, F5, 37) (dual of [657, 531, 38]-code) | [i] | ||
| 67 | Linear OA(5126, 658, F5, 37) (dual of [658, 532, 38]-code) | [i] | ||
| 68 | Linear OA(5125, 656, F5, 37) (dual of [656, 531, 38]-code) | [i] | ||
| 69 | Linear OA(5134, 679, F5, 37) (dual of [679, 545, 38]-code) | [i] | ||
| 70 | Linear OA(5141, 687, F5, 38) (dual of [687, 546, 39]-code) | [i] | ||
| 71 | Linear OA(5135, 672, F5, 38) (dual of [672, 537, 39]-code) | [i] | ||
| 72 | Linear OA(5133, 668, F5, 38) (dual of [668, 535, 39]-code) | [i] | ||
| 73 | Linear OA(5129, 656, F5, 38) (dual of [656, 527, 39]-code) | [i] | ||
| 74 | Linear OA(5130, 661, F5, 38) (dual of [661, 531, 39]-code) | [i] | ||
| 75 | Linear OA(5142, 679, F5, 39) (dual of [679, 537, 40]-code) | [i] | ||
| 76 | Linear OA(5137, 668, F5, 39) (dual of [668, 531, 40]-code) | [i] | ||
| 77 | Linear OA(5133, 656, F5, 39) (dual of [656, 523, 40]-code) | [i] | ||
| 78 | Linear OA(5134, 661, F5, 39) (dual of [661, 527, 40]-code) | [i] | ||
| 79 | Linear OA(5137, 669, F5, 39) (dual of [669, 532, 40]-code) | [i] | ||
| 80 | Linear OA(5136, 667, F5, 39) (dual of [667, 531, 40]-code) | [i] | ||
| 81 | Linear OA(5147, 682, F5, 40) (dual of [682, 535, 41]-code) | [i] | ||
| 82 | Linear OA(5141, 668, F5, 40) (dual of [668, 527, 41]-code) | [i] | ||
| 83 | Linear OA(5138, 661, F5, 40) (dual of [661, 523, 41]-code) | [i] | ||
| 84 | Linear OA(5137, 656, F5, 40) (dual of [656, 519, 41]-code) | [i] | ||
| 85 | Linear OA(5149, 682, F5, 41) (dual of [682, 533, 42]-code) | [i] | ||
| 86 | Linear OA(5143, 672, F5, 41) (dual of [672, 529, 42]-code) | [i] | ||
| 87 | Linear OA(5141, 668, F5, 41) (dual of [668, 527, 42]-code) | [i] | ||
| 88 | Linear OA(5138, 657, F5, 41) (dual of [657, 519, 42]-code) | [i] | ||
| 89 | Linear OA(5146, 678, F5, 41) (dual of [678, 532, 42]-code) | [i] | ||
| 90 | Linear OA(5141, 672, F5, 40) (dual of [672, 531, 41]-code) | [i] | ||
| 91 | Linear OA(5148, 675, F5, 42) (dual of [675, 527, 43]-code) | [i] | ||
| 92 | Linear OA(5145, 668, F5, 42) (dual of [668, 523, 43]-code) | [i] | ||
| 93 | Linear OA(5142, 657, F5, 42) (dual of [657, 515, 43]-code) | [i] | ||
| 94 | Linear OA(5142, 658, F5, 42) (dual of [658, 516, 43]-code) | [i] | ||
| 95 | Linear OA(5141, 656, F5, 42) (dual of [656, 515, 43]-code) | [i] | ||
| 96 | Linear OA(5149, 668, F5, 43) (dual of [668, 519, 44]-code) | [i] | ||
| 97 | Linear OA(5145, 656, F5, 43) (dual of [656, 511, 44]-code) | [i] | ||
| 98 | Linear OA(5146, 661, F5, 43) (dual of [661, 515, 44]-code) | [i] | ||
| 99 | Linear OA(5149, 656, F5, 44) (dual of [656, 507, 45]-code) | [i] | ||
| 100 | Linear OA(5150, 661, F5, 44) (dual of [661, 511, 45]-code) | [i] | ||