Information on Result #717983
Linear OA(972, 115, F9, 39) (dual of [115, 43, 40]-code), using construction XX applied to C1 = C([71,21]), C2 = C([0,29]), C3 = C1 + C2 = C([0,21]), and C∩ = C1 ∩ C2 = C([71,29]) based on
- linear OA(947, 80, F9, 31) (dual of [80, 33, 32]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {−9,−8,…,21}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(945, 80, F9, 30) (dual of [80, 35, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(955, 80, F9, 39) (dual of [80, 25, 40]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {−9,−8,…,29}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(935, 80, F9, 22) (dual of [80, 45, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 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
- linear OA(98, 16, F9, 7) (dual of [16, 8, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(98, 18, F9, 7) (dual of [18, 10, 8]-code), using
- 2 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(98, 18, F9, 7) (dual of [18, 10, 8]-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(971, 114, F9, 38) (dual of [114, 43, 39]-code) | [i] | Truncation | |
| 2 | Linear OA(970, 113, F9, 37) (dual of [113, 43, 38]-code) | [i] | ||
| 3 | Linear OA(969, 112, F9, 36) (dual of [112, 43, 37]-code) | [i] | ||
| 4 | Linear OOA(972, 57, F9, 2, 39) (dual of [(57, 2), 42, 40]-NRT-code) | [i] | OOA Folding | |