Information on Result #718245
Linear OA(981, 106, F9, 52) (dual of [106, 25, 53]-code), using construction XX applied to C1 = C([71,39]), C2 = C([1,42]), C3 = C1 + C2 = C([1,39]), and C∩ = C1 ∩ C2 = C([71,42]) based on
- 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(960, 80, F9, 42) (dual of [80, 20, 43]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(969, 80, F9, 52) (dual of [80, 11, 53]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {−9,−8,…,42}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(955, 80, F9, 39) (dual of [80, 25, 40]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(910, 19, F9, 9) (dual of [19, 9, 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(92, 7, F9, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,9)), using
- discarding factors / shortening the dual code based on linear OA(92, 9, F9, 2) (dual of [9, 7, 3]-code or 9-arc in PG(1,9)), using
- Reed–Solomon code RS(7,9) [i]
- discarding factors / shortening the dual code based on linear OA(92, 9, F9, 2) (dual of [9, 7, 3]-code or 9-arc in PG(1,9)), 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(981, 53, F9, 2, 52) (dual of [(53, 2), 25, 53]-NRT-code) | [i] | OOA Folding | |