Information on Result #712631
Linear OA(769, 121, F7, 32) (dual of [121, 52, 33]-code), using construction XX applied to C1 = C([112,28]), C2 = C([0,29]), C3 = C1 + C2 = C([0,28]), and C∩ = C1 ∩ C2 = C([112,29]) based on
- linear OA(765, 114, F7, 31) (dual of [114, 49, 32]-code), using the BCH-code C(I) with length 114 | 73−1, defining interval I = {−2,−1,…,28}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(765, 114, F7, 30) (dual of [114, 49, 31]-code), using the expurgated narrow-sense BCH-code C(I) with length 114 | 73−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(768, 114, F7, 32) (dual of [114, 46, 33]-code), using the BCH-code C(I) with length 114 | 73−1, defining interval I = {−2,−1,…,29}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(762, 114, F7, 29) (dual of [114, 52, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 114 | 73−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(71, 4, F7, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- Reed–Solomon code RS(6,7) [i]
- discarding factors / shortening the dual code based on linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- 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(769, 60, F7, 2, 32) (dual of [(60, 2), 51, 33]-NRT-code) | [i] | OOA Folding | |