Information on Result #714083
Linear OA(797, 355, F7, 37) (dual of [355, 258, 38]-code), using construction XX applied to C1 = C([22,56]), C2 = C([25,58]), C3 = C1 + C2 = C([25,56]), and C∩ = C1 ∩ C2 = C([22,58]) based on
- linear OA(790, 342, F7, 35) (dual of [342, 252, 36]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {22,23,…,56}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(788, 342, F7, 34) (dual of [342, 254, 35]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {25,26,…,58}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(794, 342, F7, 37) (dual of [342, 248, 38]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {22,23,…,58}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(784, 342, F7, 32) (dual of [342, 258, 33]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {25,26,…,56}, and designed minimum distance d ≥ |I|+1 = 33 [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(71, 5, F7, 1) (dual of [5, 4, 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
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(797, 177, F7, 2, 37) (dual of [(177, 2), 257, 38]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(797, 118, F7, 3, 37) (dual of [(118, 3), 257, 38]-NRT-code) | [i] | ||