Information on Result #721480
Linear OA(1682, 111, F16, 51) (dual of [111, 29, 52]-code), using construction XX applied to C1 = C([80,39]), C2 = C([4,45]), C3 = C1 + C2 = C([4,39]), and C∩ = C1 ∩ C2 = C([80,45]) based on
- linear OA(1663, 85, F16, 45) (dual of [85, 22, 46]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {−5,−4,…,39}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(1662, 85, F16, 42) (dual of [85, 23, 43]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {4,5,…,45}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(1669, 85, F16, 51) (dual of [85, 16, 52]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {−5,−4,…,45}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(1656, 85, F16, 36) (dual of [85, 29, 37]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {4,5,…,39}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(168, 15, F16, 8) (dual of [15, 7, 9]-code or 15-arc in PG(7,16)), using
- discarding factors / shortening the dual code based on linear OA(168, 16, F16, 8) (dual of [16, 8, 9]-code or 16-arc in PG(7,16)), using
- Reed–Solomon code RS(8,16) [i]
- discarding factors / shortening the dual code based on linear OA(168, 16, F16, 8) (dual of [16, 8, 9]-code or 16-arc in PG(7,16)), using
- linear OA(165, 11, F16, 5) (dual of [11, 6, 6]-code or 11-arc in PG(4,16)), using
- discarding factors / shortening the dual code based on linear OA(165, 16, F16, 5) (dual of [16, 11, 6]-code or 16-arc in PG(4,16)), using
- Reed–Solomon code RS(11,16) [i]
- discarding factors / shortening the dual code based on linear OA(165, 16, F16, 5) (dual of [16, 11, 6]-code or 16-arc in PG(4,16)), 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(1681, 110, F16, 50) (dual of [110, 29, 51]-code) | [i] | Truncation | |
| 2 | Linear OOA(1682, 55, F16, 2, 51) (dual of [(55, 2), 28, 52]-NRT-code) | [i] | OOA Folding | |