Information on Result #722090
Linear OA(16107, 278, F16, 57) (dual of [278, 171, 58]-code), using construction XX applied to C1 = C([252,50]), C2 = C([5,53]), C3 = C1 + C2 = C([5,50]), and C∩ = C1 ∩ C2 = C([252,53]) based on
- linear OA(1693, 255, F16, 54) (dual of [255, 162, 55]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−3,−2,…,50}, and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(1689, 255, F16, 49) (dual of [255, 166, 50]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {5,6,…,53}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(1698, 255, F16, 57) (dual of [255, 157, 58]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−3,−2,…,53}, and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(1684, 255, F16, 46) (dual of [255, 171, 47]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {5,6,…,50}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(167, 16, F16, 7) (dual of [16, 9, 8]-code or 16-arc in PG(6,16)), using
- Reed–Solomon code RS(9,16) [i]
- linear OA(162, 7, F16, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), 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(16107, 139, F16, 2, 57) (dual of [(139, 2), 171, 58]-NRT-code) | [i] | OOA Folding | |