Information on Result #714402
Linear OA(783, 813, F7, 25) (dual of [813, 730, 26]-code), using construction XX applied to C1 = C([131,154]), C2 = C([130,152]), C3 = C1 + C2 = C([131,152]), and C∩ = C1 ∩ C2 = C([130,154]) based on
- linear OA(778, 800, F7, 24) (dual of [800, 722, 25]-code), using the BCH-code C(I) with length 800 | 74−1, defining interval I = {131,132,…,154}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(774, 800, F7, 23) (dual of [800, 726, 24]-code), using the BCH-code C(I) with length 800 | 74−1, defining interval I = {130,131,…,152}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(782, 800, F7, 25) (dual of [800, 718, 26]-code), using the BCH-code C(I) with length 800 | 74−1, defining interval I = {130,131,…,154}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(770, 800, F7, 22) (dual of [800, 730, 23]-code), using the BCH-code C(I) with length 800 | 74−1, defining interval I = {131,132,…,152}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(71, 9, F7, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- linear OA(70, 4, F7, 0) (dual of [4, 4, 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(783, 406, F7, 2, 25) (dual of [(406, 2), 729, 26]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(783, 271, F7, 3, 25) (dual of [(271, 3), 730, 26]-NRT-code) | [i] | ||