Information on Result #686555
Linear OA(8170, 262187, F8, 31) (dual of [262187, 262017, 32]-code), using construction X applied to Ce(30) ⊂ Ce(24) based on
- linear OA(8163, 262144, F8, 31) (dual of [262144, 261981, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(8127, 262144, F8, 25) (dual of [262144, 262017, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(87, 43, F8, 5) (dual of [43, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(8171, 262188, F8, 31) (dual of [262188, 262017, 32]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8172, 262189, F8, 31) (dual of [262189, 262017, 32]-code) | [i] | ||
| 3 | Linear OA(8173, 262190, F8, 31) (dual of [262190, 262017, 32]-code) | [i] | ||
| 4 | Linear OOA(8170, 262187, F8, 2, 31) (dual of [(262187, 2), 524204, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(8170, 262187, F8, 3, 31) (dual of [(262187, 3), 786391, 32]-NRT-code) | [i] | ||
| 6 | Digital (139, 170, 262187)-net over F8 | [i] | ||
| 7 | Linear OA(8171, 262189, F8, 31) (dual of [262189, 262018, 32]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OA(8172, 262191, F8, 31) (dual of [262191, 262019, 32]-code) | [i] | ||
| 9 | Linear OOA(8170, 131093, F8, 2, 31) (dual of [(131093, 2), 262016, 32]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(8170, 87395, F8, 3, 31) (dual of [(87395, 3), 262015, 32]-NRT-code) | [i] | ||
| 11 | Linear OOA(8170, 17479, F8, 31, 31) (dual of [(17479, 31), 541679, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |