Information on Result #718290
Linear OA(990, 112, F9, 59) (dual of [112, 22, 60]-code), using construction XX applied to C1 = C([10,59]), C2 = C([1,49]), C3 = C1 + C2 = C([10,49]), and C∩ = C1 ∩ C2 = C([1,59]) based on
- linear OA(965, 80, F9, 50) (dual of [80, 15, 51]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {10,11,…,59}, and designed minimum distance d ≥ |I|+1 = 51 [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(971, 80, F9, 59) (dual of [80, 9, 60]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,59], and designed minimum distance d ≥ |I|+1 = 60 [i]
- linear OA(956, 80, F9, 40) (dual of [80, 24, 41]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {10,11,…,49}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(910, 17, F9, 9) (dual of [17, 7, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(910, 20, F9, 9) (dual of [20, 10, 10]-code), using
- extended quadratic residue code Qe(20,9) [i]
- discarding factors / shortening the dual code based on linear OA(910, 20, F9, 9) (dual of [20, 10, 10]-code), using
- linear OA(99, 15, F9, 8) (dual of [15, 6, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(99, 19, F9, 8) (dual of [19, 10, 9]-code), using
- 1 times truncation [i] based on linear OA(910, 20, F9, 9) (dual of [20, 10, 10]-code) (see above)
- discarding factors / shortening the dual code based on linear OA(99, 19, F9, 8) (dual of [19, 10, 9]-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(989, 111, F9, 58) (dual of [111, 22, 59]-code) | [i] | Truncation | |
| 2 | Linear OA(988, 110, F9, 57) (dual of [110, 22, 58]-code) | [i] | ||
| 3 | Linear OA(987, 109, F9, 56) (dual of [109, 22, 57]-code) | [i] | ||
| 4 | Linear OA(986, 108, F9, 55) (dual of [108, 22, 56]-code) | [i] | ||
| 5 | Linear OOA(990, 56, F9, 2, 59) (dual of [(56, 2), 22, 60]-NRT-code) | [i] | OOA Folding | |