Information on Result #713082
Linear OA(7109, 201, F7, 45) (dual of [201, 92, 46]-code), using construction XX applied to C1 = C([15,57]), C2 = C([22,60]), C3 = C1 + C2 = C([22,57]), and C∩ = C1 ∩ C2 = C([15,60]) based on
- linear OA(794, 171, F7, 43) (dual of [171, 77, 44]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {15,16,…,57}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(785, 171, F7, 39) (dual of [171, 86, 40]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {22,23,…,60}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(7100, 171, F7, 46) (dual of [171, 71, 47]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {15,16,…,60}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(779, 171, F7, 36) (dual of [171, 92, 37]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {22,23,…,57}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(77, 22, F7, 5) (dual of [22, 15, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-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 OA(7110, 202, F7, 45) (dual of [202, 92, 46]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(7109, 100, F7, 2, 45) (dual of [(100, 2), 91, 46]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(7109, 67, F7, 3, 45) (dual of [(67, 3), 92, 46]-NRT-code) | [i] | ||