Information on Result #715230
Linear OA(852, 524, F8, 19) (dual of [524, 472, 20]-code), using construction XX applied to C1 = C([56,73]), C2 = C([60,74]), C3 = C1 + C2 = C([60,73]), and C∩ = C1 ∩ C2 = C([56,74]) based on
- 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 = {56,57,…,73}, 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 = {60,61,…,74}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(849, 511, F8, 19) (dual of [511, 462, 20]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {56,57,…,74}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- 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 = {60,61,…,73}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(83, 10, F8, 3) (dual of [10, 7, 4]-code or 10-arc in PG(2,8) or 10-cap in PG(2,8)), 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(852, 516, F8, 2, 19) (dual of [(516, 2), 980, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(852, 516, F8, 3, 19) (dual of [(516, 3), 1496, 20]-NRT-code) | [i] | ||
| 3 | Digital (33, 52, 516)-net over F8 | [i] | ||