Information on Result #718832
Linear OA(918, 741, F9, 6) (dual of [741, 723, 7]-code), using construction XX applied to C1 = C([725,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([725,2]) based on
- linear OA(913, 728, F9, 5) (dual of [728, 715, 6]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−3,−2,−1,0,1}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(97, 728, F9, 3) (dual of [728, 721, 4]-code or 728-cap in PG(6,9)), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(916, 728, F9, 6) (dual of [728, 712, 7]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−3,−2,…,2}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(94, 728, F9, 2) (dual of [728, 724, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(92, 10, F9, 2) (dual of [10, 8, 3]-code or 10-arc in PG(1,9)), using
- extended Reed–Solomon code RSe(8,9) [i]
- Hamming code H(2,9) [i]
- linear OA(90, 3, F9, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 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(918, 247, F9, 3, 6) (dual of [(247, 3), 723, 7]-NRT-code) | [i] | OOA Folding | |