Information on Result #686811
Linear OA(8129, 32786, F8, 29) (dual of [32786, 32657, 30]-code), using construction X applied to Ce(28) ⊂ Ce(25) based on
- linear OA(8126, 32768, F8, 29) (dual of [32768, 32642, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(8111, 32768, F8, 26) (dual of [32768, 32657, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(83, 18, F8, 2) (dual of [18, 15, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-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 OOA(8129, 29812, F8, 2, 29) (dual of [(29812, 2), 59495, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8129, 29812, F8, 3, 29) (dual of [(29812, 3), 89307, 30]-NRT-code) | [i] | ||
| 3 | Digital (100, 129, 29812)-net over F8 | [i] | ||
| 4 | Linear OOA(8129, 16393, F8, 2, 29) (dual of [(16393, 2), 32657, 30]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8129, 10928, F8, 3, 29) (dual of [(10928, 3), 32655, 30]-NRT-code) | [i] | ||