Information on Result #713155
Linear OA(7104, 178, F7, 47) (dual of [178, 74, 48]-code), using construction XX applied to C1 = C([15,60]), C2 = C([14,58]), C3 = C1 + C2 = C([15,58]), and C∩ = C1 ∩ C2 = C([14,60]) based on
- linear OA(7100, 171, F7, 46) (dual of [171, 71, 47]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {15,16,…,60}, and designed minimum distance d ≥ |I|+1 = 47 [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(7103, 171, F7, 47) (dual of [171, 68, 48]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {14,15,…,60}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(797, 171, F7, 44) (dual of [171, 74, 45]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {15,16,…,58}, and designed minimum distance d ≥ |I|+1 = 45 [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(7104, 89, F7, 2, 47) (dual of [(89, 2), 74, 48]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(7104, 59, F7, 3, 47) (dual of [(59, 3), 73, 48]-NRT-code) | [i] | ||