Information on Result #714384
Linear OA(768, 812, F7, 20) (dual of [812, 744, 21]-code), using construction XX applied to C1 = C([134,152]), C2 = C([133,149]), C3 = C1 + C2 = C([134,149]), and C∩ = C1 ∩ C2 = C([133,152]) based on
- linear OA(762, 800, F7, 19) (dual of [800, 738, 20]-code), using the BCH-code C(I) with length 800 | 74−1, defining interval I = {134,135,…,152}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(760, 800, F7, 17) (dual of [800, 740, 18]-code), using the BCH-code C(I) with length 800 | 74−1, defining interval I = {133,134,…,149}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(766, 800, F7, 20) (dual of [800, 734, 21]-code), using the BCH-code C(I) with length 800 | 74−1, defining interval I = {133,134,…,152}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(756, 800, F7, 16) (dual of [800, 744, 17]-code), using the BCH-code C(I) with length 800 | 74−1, defining interval I = {134,135,…,149}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(72, 8, F7, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,7)), using
- extended Reed–Solomon code RSe(6,7) [i]
- Hamming code H(2,7) [i]
- algebraic-geometric code AG(F, Q+1P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F7 with g(F) = 0 and N(F) ≥ 8, using the rational function field F7(x) [i]
- 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(768, 406, F7, 2, 20) (dual of [(406, 2), 744, 21]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(768, 270, F7, 3, 20) (dual of [(270, 3), 742, 21]-NRT-code) | [i] | ||