Information on Result #713258
Linear OA(728, 357, F7, 10) (dual of [357, 329, 11]-code), using construction XX applied to C1 = C([50,57]), C2 = C([53,59]), C3 = C1 + C2 = C([53,57]), and C∩ = C1 ∩ C2 = C([50,59]) based on
- linear OA(719, 342, F7, 8) (dual of [342, 323, 9]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {50,51,…,57}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(719, 342, F7, 7) (dual of [342, 323, 8]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {53,54,…,59}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(725, 342, F7, 10) (dual of [342, 317, 11]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {50,51,…,59}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(713, 342, F7, 5) (dual of [342, 329, 6]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {53,54,55,56,57}, and designed minimum distance d ≥ |I|+1 = 6 [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, 7, F7, 1) (dual of [7, 6, 2]-code), using
- Reed–Solomon code RS(6,7) [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(728, 178, F7, 2, 10) (dual of [(178, 2), 328, 11]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(728, 119, F7, 3, 10) (dual of [(119, 3), 329, 11]-NRT-code) | [i] | ||