Information on Result #686819
Linear OA(889, 32786, F8, 20) (dual of [32786, 32697, 21]-code), using construction X applied to Ce(19) ⊂ Ce(16) based on
- linear OA(886, 32768, F8, 20) (dual of [32768, 32682, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- 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(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 OA(890, 32787, F8, 20) (dual of [32787, 32697, 21]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(889, 28053, F8, 2, 20) (dual of [(28053, 2), 56017, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(889, 28053, F8, 3, 20) (dual of [(28053, 3), 84070, 21]-NRT-code) | [i] | ||
| 4 | Digital (69, 89, 28053)-net over F8 | [i] | ||
| 5 | Linear OOA(889, 16393, F8, 2, 20) (dual of [(16393, 2), 32697, 21]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(889, 10928, F8, 3, 20) (dual of [(10928, 3), 32695, 21]-NRT-code) | [i] | ||