Information on Result #715282
Linear OA(847, 518, F8, 18) (dual of [518, 471, 19]-code), using construction XX applied to C1 = C([57,73]), C2 = C([59,74]), C3 = C1 + C2 = C([59,73]), and C∩ = C1 ∩ C2 = C([57,74]) based on
- linear OA(843, 511, F8, 17) (dual of [511, 468, 18]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {57,58,…,73}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(843, 511, F8, 16) (dual of [511, 468, 17]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {59,60,…,74}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(846, 511, F8, 18) (dual of [511, 465, 19]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {57,58,…,74}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(840, 511, F8, 15) (dual of [511, 471, 16]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {59,60,…,73}, and designed minimum distance d ≥ |I|+1 = 16 [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(847, 375, F8, 2, 18) (dual of [(375, 2), 703, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(847, 375, F8, 3, 18) (dual of [(375, 3), 1078, 19]-NRT-code) | [i] | ||
| 3 | Digital (29, 47, 375)-net over F8 | [i] | ||
| 4 | Linear OOA(847, 259, F8, 2, 18) (dual of [(259, 2), 471, 19]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(847, 172, F8, 3, 18) (dual of [(172, 3), 469, 19]-NRT-code) | [i] | ||