Information on Result #718195
Linear OA(977, 107, F9, 46) (dual of [107, 30, 47]-code), using construction XX applied to C1 = C([71,31]), C2 = C([0,39]), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C([71,39]) based on
- linear OA(958, 80, F9, 41) (dual of [80, 22, 42]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {−9,−8,…,31}, and designed minimum distance d ≥ |I|+1 = 42 [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(964, 80, F9, 49) (dual of [80, 16, 50]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {−9,−8,…,39}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(948, 80, F9, 32) (dual of [80, 32, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(99, 17, F9, 8) (dual of [17, 8, 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
- 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]
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(977, 53, F9, 2, 46) (dual of [(53, 2), 29, 47]-NRT-code) | [i] | OOA Folding | |