Information on Result #712578
Linear OA(756, 130, F7, 23) (dual of [130, 74, 24]-code), using construction XX applied to C1 = C([0,19]), C2 = C([5,22]), C3 = C1 + C2 = C([5,19]), and C∩ = C1 ∩ C2 = C([0,22]) based on
- linear OA(744, 114, F7, 20) (dual of [114, 70, 21]-code), using the expurgated narrow-sense BCH-code C(I) with length 114 | 73−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(746, 114, F7, 18) (dual of [114, 68, 19]-code), using the BCH-code C(I) with length 114 | 73−1, defining interval I = {5,6,…,22}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(750, 114, F7, 23) (dual of [114, 64, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 114 | 73−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(737, 114, F7, 15) (dual of [114, 77, 16]-code), using the BCH-code C(I) with length 114 | 73−1, defining interval I = {5,6,…,19}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(74, 8, F7, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,7)), using
- extended Reed–Solomon code RSe(4,7) [i]
- algebraic-geometric code AG(F, Q+0P) 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(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 (see above)
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(756, 65, F7, 2, 23) (dual of [(65, 2), 74, 24]-NRT-code) | [i] | OOA Folding | |