Information on Result #722386
Linear OA(16121, 268, F16, 70) (dual of [268, 147, 71]-code), using construction XX applied to C1 = C([0,68]), C2 = C([7,69]), C3 = C1 + C2 = C([7,68]), and C∩ = C1 ∩ C2 = C([0,69]) based on
- linear OA(16113, 255, F16, 69) (dual of [255, 142, 70]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,68], and designed minimum distance d ≥ |I|+1 = 70 [i]
- linear OA(16110, 255, F16, 63) (dual of [255, 145, 64]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {7,8,…,69}, and designed minimum distance d ≥ |I|+1 = 64 [i]
- linear OA(16115, 255, F16, 70) (dual of [255, 140, 71]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,69], and designed minimum distance d ≥ |I|+1 = 71 [i]
- linear OA(16108, 255, F16, 62) (dual of [255, 147, 63]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {7,8,…,68}, and designed minimum distance d ≥ |I|+1 = 63 [i]
- linear OA(166, 11, F16, 6) (dual of [11, 5, 7]-code or 11-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
- linear OA(160, 2, F16, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(16121, 134, F16, 2, 70) (dual of [(134, 2), 147, 71]-NRT-code) | [i] | OOA Folding | |