Information on Result #717664
Linear OA(934, 90, F9, 18) (dual of [90, 56, 19]-code), using construction XX applied to C1 = C([77,13]), C2 = C([0,14]), C3 = C1 + C2 = C([0,13]), and C∩ = C1 ∩ C2 = C([77,14]) based on
- linear OA(930, 80, F9, 17) (dual of [80, 50, 18]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {−3,−2,…,13}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(926, 80, F9, 15) (dual of [80, 54, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(932, 80, F9, 18) (dual of [80, 48, 19]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {−3,−2,…,14}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(924, 80, F9, 14) (dual of [80, 56, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(92, 8, F9, 2) (dual of [8, 6, 3]-code or 8-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
- 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(934, 45, F9, 2, 18) (dual of [(45, 2), 56, 19]-NRT-code) | [i] | OOA Folding | |