Information on Result #721485
Linear OA(1685, 114, F16, 52) (dual of [114, 29, 53]-code), using construction XX applied to C1 = C([80,39]), C2 = C([4,46]), C3 = C1 + C2 = C([4,39]), and C∩ = C1 ∩ C2 = C([80,46]) 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(1664, 85, F16, 43) (dual of [85, 21, 44]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {4,5,…,46}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(1671, 85, F16, 52) (dual of [85, 14, 53]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {−5,−4,…,46}, and designed minimum distance d ≥ |I|+1 = 53 [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(166, 14, F16, 6) (dual of [14, 8, 7]-code or 14-arc in PG(5,16)), using
- discarding factors / shortening the dual code based on linear OA(166, 16, F16, 6) (dual of [16, 10, 7]-code or 16-arc in PG(5,16)), using
- Reed–Solomon code RS(10,16) [i]
- discarding factors / shortening the dual code based on linear OA(166, 16, F16, 6) (dual of [16, 10, 7]-code or 16-arc in PG(5,16)), 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 OOA(1685, 57, F16, 2, 52) (dual of [(57, 2), 29, 53]-NRT-code) | [i] | OOA Folding | |