Information on Result #718012
Linear OA(972, 111, F9, 40) (dual of [111, 39, 41]-code), using construction XX applied to C1 = C([7,39]), C2 = C([0,30]), C3 = C1 + C2 = C([7,30]), and C∩ = C1 ∩ C2 = C([0,39]) based on
- 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(946, 80, F9, 31) (dual of [80, 34, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,30], and designed minimum distance d ≥ |I|+1 = 32 [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(939, 80, F9, 24) (dual of [80, 41, 25]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {7,8,…,30}, and designed minimum distance d ≥ |I|+1 = 25 [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(97, 12, F9, 6) (dual of [12, 5, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(97, 17, F9, 6) (dual of [17, 10, 7]-code), using
- 3 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(97, 17, F9, 6) (dual of [17, 10, 7]-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(972, 55, F9, 2, 40) (dual of [(55, 2), 38, 41]-NRT-code) | [i] | OOA Folding | |