Information on Result #687164
Linear OA(8137, 4100, F8, 39) (dual of [4100, 3963, 40]-code), using construction X applied to Ce(38) ⊂ Ce(37) based on
- linear OA(8137, 4096, F8, 39) (dual of [4096, 3959, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(8133, 4096, F8, 38) (dual of [4096, 3963, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(80, 4, F8, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(8137, 4100, F8, 2, 39) (dual of [(4100, 2), 8063, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8137, 4100, F8, 3, 39) (dual of [(4100, 3), 12163, 40]-NRT-code) | [i] | ||
| 3 | Digital (98, 137, 4100)-net over F8 | [i] | ||
| 4 | Linear OA(8138, 4171, F8, 39) (dual of [4171, 4033, 40]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OA(8139, 4347, F8, 39) (dual of [4347, 4208, 40]-code) | [i] | ||
| 6 | Linear OA(8140, 4580, F8, 39) (dual of [4580, 4440, 40]-code) | [i] | ||
| 7 | Linear OA(8141, 4835, F8, 39) (dual of [4835, 4694, 40]-code) | [i] | ||
| 8 | Linear OOA(8137, 2050, F8, 2, 39) (dual of [(2050, 2), 3963, 40]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(8137, 1366, F8, 3, 39) (dual of [(1366, 3), 3961, 40]-NRT-code) | [i] | ||