Information on Result #684424
Linear OA(511, 31, F5, 6) (dual of [31, 20, 7]-code), using construction X applied to Ce(5) ⊂ Ce(2) 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(55, 25, F5, 3) (dual of [25, 20, 4]-code or 25-cap in PG(4,5)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(52, 6, F5, 2) (dual of [6, 4, 3]-code or 6-arc in PG(1,5)), using
- extended Reed–Solomon code RSe(4,5) [i]
- Hamming code H(2,5) [i]
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(564, 659, F5, 17) (dual of [659, 595, 18]-code) | [i] | Construction XX with Cyclic Codes | |
| 2 | Linear OA(569, 664, F5, 18) (dual of [664, 595, 19]-code) | [i] | ||
| 3 | Linear OA(573, 664, F5, 19) (dual of [664, 591, 20]-code) | [i] | ||
| 4 | Linear OA(577, 664, F5, 20) (dual of [664, 587, 21]-code) | [i] | ||
| 5 | Linear OA(576, 656, F5, 21) (dual of [656, 580, 22]-code) | [i] | ||
| 6 | Linear OA(584, 671, F5, 22) (dual of [671, 587, 23]-code) | [i] | ||
| 7 | Linear OA(581, 661, F5, 22) (dual of [661, 580, 23]-code) | [i] | ||
| 8 | Linear OA(580, 659, F5, 22) (dual of [659, 579, 23]-code) | [i] | ||
| 9 | Linear OA(588, 671, F5, 23) (dual of [671, 583, 24]-code) | [i] | ||
| 10 | Linear OA(584, 659, F5, 23) (dual of [659, 575, 24]-code) | [i] | ||
| 11 | Linear OA(585, 664, F5, 23) (dual of [664, 579, 24]-code) | [i] | ||
| 12 | Linear OA(592, 671, F5, 24) (dual of [671, 579, 25]-code) | [i] | ||
| 13 | Linear OA(588, 659, F5, 24) (dual of [659, 571, 25]-code) | [i] | ||
| 14 | Linear OA(589, 664, F5, 24) (dual of [664, 575, 25]-code) | [i] | ||
| 15 | Linear OA(592, 672, F5, 24) (dual of [672, 580, 25]-code) | [i] | ||
| 16 | Linear OA(591, 670, F5, 24) (dual of [670, 579, 25]-code) | [i] | ||
| 17 | Linear OA(593, 664, F5, 25) (dual of [664, 571, 26]-code) | [i] | ||
| 18 | Linear OA(595, 670, F5, 25) (dual of [670, 575, 26]-code) | [i] | ||
| 19 | Linear OA(592, 656, F5, 26) (dual of [656, 564, 27]-code) | [i] | ||
| 20 | Linear OA(596, 671, F5, 26) (dual of [671, 575, 27]-code) | [i] | ||
| 21 | Linear OA(596, 659, F5, 27) (dual of [659, 563, 28]-code) | [i] | ||
| 22 | Linear OA(5103, 661, F5, 29) (dual of [661, 558, 30]-code) | [i] | ||
| 23 | Linear OA(5107, 661, F5, 30) (dual of [661, 554, 31]-code) | [i] | ||
| 24 | Linear OA(5107, 664, F5, 30) (dual of [664, 557, 31]-code) | [i] | ||
| 25 | Linear OA(5115, 678, F5, 31) (dual of [678, 563, 32]-code) | [i] | ||
| 26 | Linear OA(5112, 671, F5, 31) (dual of [671, 559, 32]-code) | [i] | ||
| 27 | Linear OA(5123, 682, F5, 33) (dual of [682, 559, 34]-code) | [i] | ||
| 28 | Linear OA(5120, 675, F5, 33) (dual of [675, 555, 34]-code) | [i] | ||
| 29 | Linear OA(5121, 678, F5, 33) (dual of [678, 557, 34]-code) | [i] | ||
| 30 | Linear OA(5118, 671, F5, 33) (dual of [671, 553, 34]-code) | [i] | ||
| 31 | Linear OA(5127, 682, F5, 34) (dual of [682, 555, 35]-code) | [i] | ||
| 32 | Linear OA(5119, 662, F5, 34) (dual of [662, 543, 35]-code) | [i] | ||
| 33 | Linear OA(5122, 671, F5, 34) (dual of [671, 549, 35]-code) | [i] | ||
| 34 | Linear OA(5131, 682, F5, 35) (dual of [682, 551, 36]-code) | [i] | ||
| 35 | Linear OA(5123, 662, F5, 35) (dual of [662, 539, 36]-code) | [i] | ||
| 36 | Linear OA(5125, 668, F5, 35) (dual of [668, 543, 36]-code) | [i] | ||
| 37 | Linear OA(5123, 664, F5, 35) (dual of [664, 541, 36]-code) | [i] | ||
| 38 | Linear OA(5122, 656, F5, 36) (dual of [656, 534, 37]-code) | [i] | ||
| 39 | Linear OA(5132, 675, F5, 37) (dual of [675, 543, 38]-code) | [i] | ||
| 40 | Linear OA(5130, 671, F5, 37) (dual of [671, 541, 38]-code) | [i] | ||
| 41 | Linear OA(5127, 661, F5, 37) (dual of [661, 534, 38]-code) | [i] | ||
| 42 | Linear OA(5126, 659, F5, 37) (dual of [659, 533, 38]-code) | [i] | ||
| 43 | Linear OA(5135, 682, F5, 37) (dual of [682, 547, 38]-code) | [i] | ||
| 44 | Linear OA(5136, 675, F5, 38) (dual of [675, 539, 39]-code) | [i] | ||
| 45 | Linear OA(5134, 671, F5, 38) (dual of [671, 537, 39]-code) | [i] | ||
| 46 | Linear OA(5139, 682, F5, 38) (dual of [682, 543, 39]-code) | [i] | ||
| 47 | Linear OA(5131, 664, F5, 38) (dual of [664, 533, 39]-code) | [i] | ||
| 48 | Linear OA(5142, 689, F5, 38) (dual of [689, 547, 39]-code) | [i] | ||
| 49 | Linear OA(5143, 682, F5, 39) (dual of [682, 539, 40]-code) | [i] | ||
| 50 | Linear OA(5141, 678, F5, 39) (dual of [678, 537, 40]-code) | [i] | ||
| 51 | Linear OA(5138, 671, F5, 39) (dual of [671, 533, 40]-code) | [i] | ||
| 52 | Linear OA(5135, 664, F5, 39) (dual of [664, 529, 40]-code) | [i] | ||
| 53 | Linear OA(5138, 672, F5, 39) (dual of [672, 534, 40]-code) | [i] | ||
| 54 | Linear OA(5137, 670, F5, 39) (dual of [670, 533, 40]-code) | [i] | ||
| 55 | Linear OA(5148, 685, F5, 40) (dual of [685, 537, 41]-code) | [i] | ||
| 56 | Linear OA(5145, 678, F5, 40) (dual of [678, 533, 41]-code) | [i] | ||
| 57 | Linear OA(5142, 671, F5, 40) (dual of [671, 529, 41]-code) | [i] | ||
| 58 | Linear OA(5139, 664, F5, 40) (dual of [664, 525, 41]-code) | [i] | ||
| 59 | Linear OA(5141, 670, F5, 40) (dual of [670, 529, 41]-code) | [i] | ||
| 60 | Linear OA(5138, 656, F5, 41) (dual of [656, 518, 42]-code) | [i] | ||
| 61 | Linear OA(5144, 675, F5, 41) (dual of [675, 531, 42]-code) | [i] | ||
| 62 | Linear OA(5142, 673, F5, 40) (dual of [673, 531, 41]-code) | [i] | ||
| 63 | Linear OA(5142, 671, F5, 41) (dual of [671, 529, 42]-code) | [i] | ||
| 64 | Linear OA(5147, 681, F5, 41) (dual of [681, 534, 42]-code) | [i] | ||
| 65 | Linear OA(5145, 678, F5, 41) (dual of [678, 533, 42]-code) | [i] | ||
| 66 | Linear OA(5142, 675, F5, 40) (dual of [675, 533, 41]-code) | [i] | ||
| 67 | Linear OA(5149, 678, F5, 42) (dual of [678, 529, 43]-code) | [i] | ||
| 68 | Linear OA(5146, 671, F5, 42) (dual of [671, 525, 43]-code) | [i] | ||
| 69 | Linear OA(5143, 661, F5, 42) (dual of [661, 518, 43]-code) | [i] | ||
| 70 | Linear OA(5142, 659, F5, 42) (dual of [659, 517, 43]-code) | [i] | ||
| 71 | Linear OA(5150, 671, F5, 43) (dual of [671, 521, 44]-code) | [i] | ||
| 72 | Linear OA(5147, 664, F5, 43) (dual of [664, 517, 44]-code) | [i] | ||