Information on Result #686824
Linear OA(869, 32786, F8, 15) (dual of [32786, 32717, 16]-code), using construction X applied to Ce(14) ⊂ Ce(11) based on
- linear OA(866, 32768, F8, 15) (dual of [32768, 32702, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(851, 32768, F8, 12) (dual of [32768, 32717, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(869, 32786, F8, 2, 15) (dual of [(32786, 2), 65503, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(869, 32786, F8, 3, 15) (dual of [(32786, 3), 98289, 16]-NRT-code) | [i] | ||
| 3 | Digital (54, 69, 32786)-net over F8 | [i] | ||
| 4 | Linear OOA(869, 16393, F8, 2, 15) (dual of [(16393, 2), 32717, 16]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(869, 10928, F8, 3, 15) (dual of [(10928, 3), 32715, 16]-NRT-code) | [i] | ||
| 6 | Linear OOA(869, 4683, F8, 15, 15) (dual of [(4683, 15), 70176, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |