Information on Result #722224
Linear OA(16119, 288, F16, 62) (dual of [288, 169, 63]-code), using construction XX applied to C1 = C([248,50]), C2 = C([1,54]), C3 = C1 + C2 = C([1,50]), and C∩ = C1 ∩ C2 = C([248,54]) based on
- linear OA(16101, 255, F16, 58) (dual of [255, 154, 59]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−7,−6,…,50}, and designed minimum distance d ≥ |I|+1 = 59 [i]
- linear OA(1693, 255, F16, 54) (dual of [255, 162, 55]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [1,54], and designed minimum distance d ≥ |I|+1 = 55 [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,−6,…,54}, and designed minimum distance d ≥ |I|+1 = 63 [i]
- linear OA(1686, 255, F16, 50) (dual of [255, 169, 51]-code), using 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(168, 23, F16, 7) (dual of [23, 15, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(168, 24, F16, 7) (dual of [24, 16, 8]-code), using
- extended algebraic-geometric code AGe(F,16P) [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- discarding factors / shortening the dual code based on linear OA(168, 24, F16, 7) (dual of [24, 16, 8]-code), using
- linear OA(163, 10, F16, 3) (dual of [10, 7, 4]-code or 10-arc in PG(2,16) or 10-cap in PG(2,16)), using
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
- Reed–Solomon code RS(13,16) [i]
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), 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(16119, 144, F16, 2, 62) (dual of [(144, 2), 169, 63]-NRT-code) | [i] | OOA Folding | |