Information on Result #718328
Linear OA(984, 105, F9, 55) (dual of [105, 21, 56]-code), using construction XX applied to C1 = C([71,40]), C2 = C([0,49]), C3 = C1 + C2 = C([0,40]), and C∩ = C1 ∩ C2 = C([71,49]) 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 = {−9,−8,…,40}, and designed minimum distance d ≥ |I|+1 = 51 [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(971, 80, F9, 59) (dual of [80, 9, 60]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {−9,−8,…,49}, and designed minimum distance d ≥ |I|+1 = 60 [i]
- linear OA(957, 80, F9, 41) (dual of [80, 23, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(94, 10, F9, 4) (dual of [10, 6, 5]-code or 10-arc in PG(3,9)), using
- extended Reed–Solomon code RSe(6,9) [i]
- 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), using
- extended quadratic residue code Qe(20,9) [i]
- 1 times truncation [i] based on linear OA(910, 20, F9, 9) (dual of [20, 10, 10]-code), using
- 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 OOA(984, 52, F9, 2, 55) (dual of [(52, 2), 20, 56]-NRT-code) | [i] | OOA Folding | |