Information on Result #713031
Linear OA(7103, 198, F7, 43) (dual of [198, 95, 44]-code), using construction XX applied to C1 = C([25,64]), C2 = C([22,58]), C3 = C1 + C2 = C([25,58]), and C∩ = C1 ∩ C2 = C([22,64]) based on
- linear OA(788, 171, F7, 40) (dual of [171, 83, 41]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {25,26,…,64}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(782, 171, F7, 37) (dual of [171, 89, 38]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {22,23,…,58}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- 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 = {22,23,…,64}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(776, 171, F7, 34) (dual of [171, 95, 35]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {25,26,…,58}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(77, 19, F7, 5) (dual of [19, 12, 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(7104, 199, F7, 43) (dual of [199, 95, 44]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(7103, 99, F7, 2, 43) (dual of [(99, 2), 95, 44]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(7103, 66, F7, 3, 43) (dual of [(66, 3), 95, 44]-NRT-code) | [i] | ||