Information on Result #686514
Linear OA(864, 262165, F8, 12) (dual of [262165, 262101, 13]-code), using construction X applied to Ce(11) ⊂ Ce(8) based on
- linear OA(861, 262144, F8, 12) (dual of [262144, 262083, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(843, 262144, F8, 9) (dual of [262144, 262101, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(83, 21, F8, 2) (dual of [21, 18, 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(865, 262166, F8, 12) (dual of [262166, 262101, 13]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(864, 262165, F8, 2, 12) (dual of [(262165, 2), 524266, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(864, 262165, F8, 3, 12) (dual of [(262165, 3), 786431, 13]-NRT-code) | [i] | ||
| 4 | Digital (52, 64, 262165)-net over F8 | [i] | ||
| 5 | Linear OA(865, 262167, F8, 12) (dual of [262167, 262102, 13]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(866, 262169, F8, 12) (dual of [262169, 262103, 13]-code) | [i] | ||
| 7 | Linear OOA(864, 131082, F8, 2, 12) (dual of [(131082, 2), 262100, 13]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(864, 87388, F8, 3, 12) (dual of [(87388, 3), 262100, 13]-NRT-code) | [i] | ||
| 9 | Linear OOA(864, 43694, F8, 12, 12) (dual of [(43694, 12), 524264, 13]-NRT-code) | [i] | OA Folding and Stacking | |