Information on Result #721915
Linear OA(1690, 268, F16, 48) (dual of [268, 178, 49]-code), using construction XX applied to C1 = C([251,42]), C2 = C([0,43]), C3 = C1 + C2 = C([0,42]), and C∩ = C1 ∩ C2 = C([251,43]) based on
- linear OA(1685, 255, F16, 47) (dual of [255, 170, 48]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−4,−3,…,42}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(1679, 255, F16, 44) (dual of [255, 176, 45]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,43], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(1687, 255, F16, 48) (dual of [255, 168, 49]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−4,−3,…,43}, and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(1677, 255, F16, 43) (dual of [255, 178, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(163, 11, F16, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,16) or 11-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
- 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(1690, 134, F16, 2, 48) (dual of [(134, 2), 178, 49]-NRT-code) | [i] | OOA Folding | |