Information on Result #686746
Linear OA(872, 32774, F8, 17) (dual of [32774, 32702, 18]-code), using construction X applied to Ce(16) ⊂ Ce(14) based on
- linear OA(871, 32768, F8, 17) (dual of [32768, 32697, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 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(81, 6, F8, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-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 OA(871, 32773, F8, 16) (dual of [32773, 32702, 17]-code) | [i] | Truncation | |
| 2 | Linear OOA(872, 17261, F8, 2, 17) (dual of [(17261, 2), 34450, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(872, 17261, F8, 3, 17) (dual of [(17261, 3), 51711, 18]-NRT-code) | [i] | ||
| 4 | Digital (55, 72, 17261)-net over F8 | [i] | ||
| 5 | Linear OOA(872, 16387, F8, 2, 17) (dual of [(16387, 2), 32702, 18]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(872, 10924, F8, 3, 17) (dual of [(10924, 3), 32700, 18]-NRT-code) | [i] | ||