Information on Result #713113
Linear OA(7105, 189, F7, 45) (dual of [189, 84, 46]-code), using construction XX applied to C1 = C([14,56]), C2 = C([18,58]), C3 = C1 + C2 = C([18,56]), and C∩ = C1 ∩ C2 = C([14,58]) based on
- linear OA(796, 171, F7, 43) (dual of [171, 75, 44]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {14,15,…,56}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(791, 171, F7, 41) (dual of [171, 80, 42]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {18,19,…,58}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(7100, 171, F7, 45) (dual of [171, 71, 46]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {14,15,…,58}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(787, 171, F7, 39) (dual of [171, 84, 40]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {18,19,…,56}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(74, 13, F7, 3) (dual of [13, 9, 4]-code or 13-cap in PG(3,7)), using
- linear OA(71, 5, F7, 1) (dual of [5, 4, 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
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(7105, 63, F7, 3, 45) (dual of [(63, 3), 84, 46]-NRT-code) | [i] | OOA Folding | |