Information on Result #718203
Linear OA(981, 108, F9, 50) (dual of [108, 27, 51]-code), using construction XX applied to C1 = C([7,49]), C2 = C([0,39]), C3 = C1 + C2 = C([7,39]), and C∩ = C1 ∩ C2 = C([0,49]) based on
- linear OA(962, 80, F9, 43) (dual of [80, 18, 44]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {7,8,…,49}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(956, 80, F9, 40) (dual of [80, 24, 41]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,39], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(965, 80, F9, 50) (dual of [80, 15, 51]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,49], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(951, 80, F9, 33) (dual of [80, 29, 34]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {7,8,…,39}, and designed minimum distance d ≥ |I|+1 = 34 [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(96, 9, F9, 6) (dual of [9, 3, 7]-code or 9-arc in PG(5,9)), using
- Reed–Solomon code RS(3,9) [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.
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(981, 54, F9, 2, 50) (dual of [(54, 2), 27, 51]-NRT-code) | [i] | OOA Folding | |