Information on Result #692801
Linear OA(1693, 270, F16, 51) (dual of [270, 177, 52]-code), using construction X applied to Ce(50) ⊂ Ce(43) based on
- linear OA(1687, 256, F16, 51) (dual of [256, 169, 52]-code), using an extension Ce(50) of the primitive narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(1679, 256, F16, 44) (dual of [256, 177, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- 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 OA(1692, 269, F16, 50) (dual of [269, 177, 51]-code) | [i] | Truncation | |
| 2 | Linear OA(1691, 268, F16, 49) (dual of [268, 177, 50]-code) | [i] | ||
| 3 | Linear OOA(1693, 135, F16, 2, 51) (dual of [(135, 2), 177, 52]-NRT-code) | [i] | OOA Folding | |