Information on Result #718386
Linear OA(988, 104, F9, 62) (dual of [104, 16, 63]-code), using construction XX applied to C1 = C([70,49]), C2 = C([1,51]), C3 = C1 + C2 = C([1,49]), and C∩ = C1 ∩ C2 = C([70,51]) based on
- linear OA(972, 80, F9, 60) (dual of [80, 8, 61]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {−10,−9,…,49}, and designed minimum distance d ≥ |I|+1 = 61 [i]
- linear OA(967, 80, F9, 51) (dual of [80, 13, 52]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,51], and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(975, 80, F9, 62) (dual of [80, 5, 63]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {−10,−9,…,51}, and designed minimum distance d ≥ |I|+1 = 63 [i]
- linear OA(964, 80, F9, 49) (dual of [80, 16, 50]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,49], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(912, 20, F9, 10) (dual of [20, 8, 11]-code), using
- extended algebraic-geometric code AGe(F,9P) [i] based on function field F/F9 with g(F) = 2 and N(F) ≥ 20, using
- linear OA(91, 4, F9, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, 9, F9, 1) (dual of [9, 8, 2]-code), using
- Reed–Solomon code RS(8,9) [i]
- discarding factors / shortening the dual code based on linear OA(91, 9, F9, 1) (dual of [9, 8, 2]-code), using
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(988, 104, F9, 61) (dual of [104, 16, 62]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(987, 103, F9, 61) (dual of [103, 16, 62]-code) | [i] | Truncation | |
| 3 | Linear OA(986, 102, F9, 60) (dual of [102, 16, 61]-code) | [i] | ||
| 4 | Linear OOA(988, 52, F9, 2, 62) (dual of [(52, 2), 16, 63]-NRT-code) | [i] | OOA Folding | |