Information on Result #718494
Linear OA(999, 112, F9, 71) (dual of [112, 13, 72]-code), using construction XX applied to C1 = C([10,70]), C2 = C([0,60]), C3 = C1 + C2 = C([10,60]), and C∩ = C1 ∩ C2 = C([0,70]) based on
- linear OA(973, 80, F9, 61) (dual of [80, 7, 62]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {10,11,…,70}, and designed minimum distance d ≥ |I|+1 = 62 [i]
- linear OA(973, 80, F9, 61) (dual of [80, 7, 62]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,60], and designed minimum distance d ≥ |I|+1 = 62 [i]
- linear OA(978, 80, F9, 71) (dual of [80, 2, 72]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,70], and designed minimum distance d ≥ |I|+1 = 72 [i]
- linear OA(966, 80, F9, 51) (dual of [80, 14, 52]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {10,11,…,60}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(910, 16, F9, 9) (dual of [16, 6, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(910, 20, F9, 9) (dual of [20, 10, 10]-code), using
- extended quadratic residue code Qe(20,9) [i]
- discarding factors / shortening the dual code based on linear OA(910, 20, F9, 9) (dual of [20, 10, 10]-code), using
- linear OA(910, 16, F9, 9) (dual of [16, 6, 10]-code) (see above)
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(999, 56, F9, 2, 71) (dual of [(56, 2), 13, 72]-NRT-code) | [i] | OOA Folding | |