Information on Result #712924
Linear OA(7103, 204, F7, 41) (dual of [204, 101, 42]-code), using construction XX applied to C1 = C([29,68]), C2 = C([28,60]), C3 = C1 + C2 = C([29,60]), and C∩ = C1 ∩ C2 = C([28,68]) based on
- linear OA(788, 171, F7, 40) (dual of [171, 83, 41]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {29,30,…,68}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(773, 171, F7, 33) (dual of [171, 98, 34]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {28,29,…,60}, and designed minimum distance d ≥ |I|+1 = 34 [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 = {28,29,…,68}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(770, 171, F7, 32) (dual of [171, 101, 33]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {29,30,…,60}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(712, 30, F7, 7) (dual of [30, 18, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(712, 48, F7, 7) (dual of [48, 36, 8]-code), using
- the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(712, 48, F7, 7) (dual of [48, 36, 8]-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(7103, 68, F7, 3, 41) (dual of [(68, 3), 101, 42]-NRT-code) | [i] | OOA Folding | |