Information on Result #712789
Linear OA(784, 198, F7, 33) (dual of [198, 114, 34]-code), using construction XX applied to C1 = C([0,29]), C2 = C([8,32]), C3 = C1 + C2 = C([8,29]), and C∩ = C1 ∩ C2 = C([0,32]) based on
- linear OA(767, 171, F7, 30) (dual of [171, 104, 31]-code), using the expurgated narrow-sense BCH-code C(I) with length 171 | 73−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(763, 171, F7, 25) (dual of [171, 108, 26]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {8,9,…,32}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(773, 171, F7, 33) (dual of [171, 98, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 171 | 73−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(757, 171, F7, 22) (dual of [171, 114, 23]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {8,9,…,29}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(79, 19, F7, 7) (dual of [19, 10, 8]-code), using
- 1 times truncation [i] based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- extended quadratic residue code Qe(20,7) [i]
- 1 times truncation [i] based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-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 OOA(784, 99, F7, 2, 33) (dual of [(99, 2), 114, 34]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(784, 66, F7, 3, 33) (dual of [(66, 3), 114, 34]-NRT-code) | [i] | ||