Information on Result #712569
Linear OA(751, 126, F7, 21) (dual of [126, 75, 22]-code), using construction XX applied to C1 = C([1,18]), C2 = C([5,21]), C3 = C1 + C2 = C([5,18]), and C∩ = C1 ∩ C2 = C([1,21]) based on
- linear OA(742, 114, F7, 18) (dual of [114, 72, 19]-code), using the narrow-sense BCH-code C(I) with length 114 | 73−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(743, 114, F7, 17) (dual of [114, 71, 18]-code), using the BCH-code C(I) with length 114 | 73−1, defining interval I = {5,6,…,21}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(746, 114, F7, 21) (dual of [114, 68, 22]-code), using the narrow-sense BCH-code C(I) with length 114 | 73−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(736, 114, F7, 14) (dual of [114, 78, 15]-code), using the BCH-code C(I) with length 114 | 73−1, defining interval I = {5,6,…,18}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(73, 6, F7, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,7) or 6-cap in PG(2,7)), using
- discarding factors / shortening the dual code based on linear OA(73, 7, F7, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,7) or 7-cap in PG(2,7)), using
- Reed–Solomon code RS(4,7) [i]
- discarding factors / shortening the dual code based on linear OA(73, 7, F7, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,7) or 7-cap in PG(2,7)), using
- linear OA(72, 6, F7, 2) (dual of [6, 4, 3]-code or 6-arc in PG(1,7)), using
- discarding factors / shortening the dual code based on linear OA(72, 7, F7, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)), using
- Reed–Solomon code RS(5,7) [i]
- discarding factors / shortening the dual code based on linear OA(72, 7, F7, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)), 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(751, 63, F7, 2, 21) (dual of [(63, 2), 75, 22]-NRT-code) | [i] | OOA Folding | |