Information on Result #715030
Linear OA(826, 518, F8, 10) (dual of [518, 492, 11]-code), using construction XX applied to C1 = C([65,73]), C2 = C([67,74]), C3 = C1 + C2 = C([67,73]), and C∩ = C1 ∩ C2 = C([65,74]) based on
- linear OA(822, 511, F8, 9) (dual of [511, 489, 10]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {65,66,…,73}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(822, 511, F8, 8) (dual of [511, 489, 9]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {67,68,…,74}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(825, 511, F8, 10) (dual of [511, 486, 11]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {65,66,…,74}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(819, 511, F8, 7) (dual of [511, 492, 8]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {67,68,…,73}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(81, 4, F8, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-code), using
- Reed–Solomon code RS(7,8) [i]
- discarding factors / shortening the dual code based on linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-code), using
- 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: 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(826, 353, F8, 2, 10) (dual of [(353, 2), 680, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(826, 353, F8, 3, 10) (dual of [(353, 3), 1033, 11]-NRT-code) | [i] | ||
| 3 | Digital (16, 26, 353)-net over F8 | [i] | ||
| 4 | Linear OOA(826, 259, F8, 2, 10) (dual of [(259, 2), 492, 11]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(826, 172, F8, 3, 10) (dual of [(172, 3), 490, 11]-NRT-code) | [i] | ||