Information on Result #718928
Linear OA(931, 741, F9, 11) (dual of [741, 710, 12]-code), using construction XX applied to C1 = C([0,9]), C2 = C([4,10]), C3 = C1 + C2 = C([4,9]), and C∩ = C1 ∩ C2 = C([0,10]) based on
- linear OA(925, 728, F9, 10) (dual of [728, 703, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(921, 728, F9, 7) (dual of [728, 707, 8]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {4,5,…,10}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(928, 728, F9, 11) (dual of [728, 700, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(918, 728, F9, 6) (dual of [728, 710, 7]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {4,5,…,9}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(93, 10, F9, 3) (dual of [10, 7, 4]-code or 10-arc in PG(2,9) or 10-cap in PG(2,9)), using
- extended Reed–Solomon code RSe(7,9) [i]
- oval in PG(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(931, 370, F9, 2, 11) (dual of [(370, 2), 709, 12]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(931, 247, F9, 3, 11) (dual of [(247, 3), 710, 12]-NRT-code) | [i] | ||