Information on Result #686870
Linear OA(8137, 32799, F8, 30) (dual of [32799, 32662, 31]-code), using construction X applied to Ce(29) ⊂ Ce(24) based on
- linear OA(8131, 32768, F8, 30) (dual of [32768, 32637, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(86, 31, F8, 4) (dual of [31, 25, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-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(8138, 32800, F8, 30) (dual of [32800, 32662, 31]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8139, 32801, F8, 30) (dual of [32801, 32662, 31]-code) | [i] | ||
| 3 | Linear OA(8140, 32802, F8, 30) (dual of [32802, 32662, 31]-code) | [i] | ||
| 4 | Linear OOA(8137, 32799, F8, 2, 30) (dual of [(32799, 2), 65461, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(8137, 32799, F8, 3, 30) (dual of [(32799, 3), 98260, 31]-NRT-code) | [i] | ||
| 6 | Digital (107, 137, 32799)-net over F8 | [i] | ||
| 7 | Linear OOA(8137, 16399, F8, 2, 30) (dual of [(16399, 2), 32661, 31]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(8137, 10933, F8, 3, 30) (dual of [(10933, 3), 32662, 31]-NRT-code) | [i] | ||