Information on Result #721988
Linear OA(16101, 278, F16, 54) (dual of [278, 177, 55]-code), using construction XX applied to C1 = C([0,50]), C2 = C([8,53]), C3 = C1 + C2 = C([8,50]), and C∩ = C1 ∩ C2 = C([0,53]) based on
- linear OA(1687, 255, F16, 51) (dual of [255, 168, 52]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,50], and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(1683, 255, F16, 46) (dual of [255, 172, 47]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {8,9,…,53}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(1692, 255, F16, 54) (dual of [255, 163, 55]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,53], and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(1678, 255, F16, 43) (dual of [255, 177, 44]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {8,9,…,50}, and designed minimum distance d ≥ |I|+1 = 44 [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(16101, 139, F16, 2, 54) (dual of [(139, 2), 177, 55]-NRT-code) | [i] | OOA Folding | |