Information on Result #718277
Linear OA(983, 104, F9, 54) (dual of [104, 21, 55]-code), using construction XX applied to C1 = C([10,61]), C2 = C([8,51]), C3 = C1 + C2 = C([10,51]), and C∩ = C1 ∩ C2 = C([8,61]) based on
- linear OA(968, 80, F9, 52) (dual of [80, 12, 53]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {10,11,…,61}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(963, 80, F9, 44) (dual of [80, 17, 45]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {8,9,…,51}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(972, 80, F9, 54) (dual of [80, 8, 55]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {8,9,…,61}, and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(959, 80, F9, 42) (dual of [80, 21, 43]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {10,11,…,51}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(910, 19, F9, 9) (dual of [19, 9, 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(91, 5, F9, 1) (dual of [5, 4, 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 OOA(983, 52, F9, 2, 54) (dual of [(52, 2), 21, 55]-NRT-code) | [i] | OOA Folding | |