Information on Result #686497
Linear OA(8166, 262165, F8, 31) (dual of [262165, 261999, 32]-code), using construction X applied to Ce(30) ⊂ Ce(27) based on
- linear OA(8163, 262144, F8, 31) (dual of [262144, 261981, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(8145, 262144, F8, 28) (dual of [262144, 261999, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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 OOA(8166, 229225, F8, 2, 31) (dual of [(229225, 2), 458284, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8166, 229225, F8, 3, 31) (dual of [(229225, 3), 687509, 32]-NRT-code) | [i] | ||
| 3 | Digital (135, 166, 229225)-net over F8 | [i] | ||
| 4 | Linear OOA(8166, 131082, F8, 2, 31) (dual of [(131082, 2), 261998, 32]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8166, 87388, F8, 3, 31) (dual of [(87388, 3), 261998, 32]-NRT-code) | [i] | ||