Information on Result #1303034
Linear OA(8166, 262186, F8, 30) (dual of [262186, 262020, 31]-code), using construction X with Varšamov bound based on
- linear OA(8163, 262180, F8, 30) (dual of [262180, 262017, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- linear OA(8157, 262144, F8, 30) (dual of [262144, 261987, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(8127, 262144, F8, 25) (dual of [262144, 262017, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(86, 36, F8, 4) (dual of [36, 30, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- linear OA(8163, 262183, F8, 29) (dual of [262183, 262020, 30]-code), using Gilbert–Varšamov bound and bm = 8163 > Vbs−1(k−1) = 79 225534 522668 794919 849743 214776 354635 507189 234292 265800 414542 250075 954864 306244 428202 720652 330637 380882 227707 064153 271539 387705 369649 943091 453348 [i]
- linear OA(80, 3, F8, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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, 262186, F8, 2, 30) (dual of [(262186, 2), 524206, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8166, 262186, F8, 3, 30) (dual of [(262186, 3), 786392, 31]-NRT-code) | [i] | ||
| 3 | Digital (136, 166, 262186)-net over F8 | [i] | ||
| 4 | Linear OOA(8166, 131093, F8, 2, 30) (dual of [(131093, 2), 262020, 31]-NRT-code) | [i] | OOA Folding | |