Information on Result #712769
Linear OA(772, 182, F7, 30) (dual of [182, 110, 31]-code), using construction XX applied to C1 = C([0,28]), C2 = C([6,29]), C3 = C1 + C2 = C([6,28]), and C∩ = C1 ∩ C2 = C([0,29]) based on
- linear OA(764, 171, F7, 29) (dual of [171, 107, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 171 | 73−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(763, 171, F7, 24) (dual of [171, 108, 25]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {6,7,…,29}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(767, 171, F7, 30) (dual of [171, 104, 31]-code), using the expurgated narrow-sense BCH-code C(I) with length 171 | 73−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(760, 171, F7, 23) (dual of [171, 111, 24]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {6,7,…,28}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(75, 8, F7, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,7)), using
- extended Reed–Solomon code RSe(3,7) [i]
- the expurgated narrow-sense BCH-code C(I) with length 8 | 72−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 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(772, 91, F7, 2, 30) (dual of [(91, 2), 110, 31]-NRT-code) | [i] | OOA Folding | |