Information on Result #715110
Linear OA(852, 541, F8, 17) (dual of [541, 489, 18]-code), using construction XX applied to C1 = C([68,81]), C2 = C([65,75]), C3 = C1 + C2 = C([68,75]), and C∩ = C1 ∩ C2 = C([65,81]) based on
- linear OA(837, 511, F8, 14) (dual of [511, 474, 15]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {68,69,…,81}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(828, 511, F8, 11) (dual of [511, 483, 12]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {65,66,…,75}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- 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 = {65,66,…,81}, and designed minimum distance d ≥ |I|+1 = 18 [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 = {68,69,…,75}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(87, 22, F8, 5) (dual of [22, 15, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- linear OA(82, 8, F8, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,8)), using
- Reed–Solomon code RS(6,8) [i]
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(853, 542, F8, 17) (dual of [542, 489, 18]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(852, 270, F8, 2, 17) (dual of [(270, 2), 488, 18]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(852, 180, F8, 3, 17) (dual of [(180, 3), 488, 18]-NRT-code) | [i] | ||