Information on Result #712797
Linear OA(780, 193, F7, 32) (dual of [193, 113, 33]-code), using construction XX applied to C1 = C([29,57]), C2 = C([36,60]), C3 = C1 + C2 = C([36,57]), and C∩ = C1 ∩ C2 = C([29,60]) based on
- linear OA(764, 171, F7, 29) (dual of [171, 107, 30]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {29,30,…,57}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(764, 171, F7, 25) (dual of [171, 107, 26]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {36,37,…,60}, and designed minimum distance d ≥ |I|+1 = 26 [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(755, 171, F7, 22) (dual of [171, 116, 23]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {36,37,…,57}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(78, 14, F7, 6) (dual of [14, 6, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(78, 19, F7, 6) (dual of [19, 11, 7]-code), using
- 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]
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(780, 96, F7, 2, 32) (dual of [(96, 2), 112, 33]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(780, 64, F7, 3, 32) (dual of [(64, 3), 112, 33]-NRT-code) | [i] | ||