Information on Result #718089
Linear OA(968, 100, F9, 42) (dual of [100, 32, 43]-code), using construction XX applied to C1 = C([0,40]), C2 = C([9,41]), C3 = C1 + C2 = C([9,40]), and C∩ = C1 ∩ C2 = C([0,41]) based on
- 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(950, 80, F9, 33) (dual of [80, 30, 34]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {9,10,…,41}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(959, 80, F9, 42) (dual of [80, 21, 43]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,41], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(948, 80, F9, 32) (dual of [80, 32, 33]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {9,10,…,40}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(99, 18, F9, 8) (dual of [18, 9, 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(90, 2, F9, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(968, 50, F9, 2, 42) (dual of [(50, 2), 32, 43]-NRT-code) | [i] | OOA Folding | |