Information on Result #722539
Linear OA(16129, 607, F16, 47) (dual of [607, 478, 48]-code), using construction XX applied to C1 = C([581,40]), C2 = C([0,42]), C3 = C1 + C2 = C([0,40]), and C∩ = C1 ∩ C2 = C([581,42]) based on
- linear OA(16119, 585, F16, 45) (dual of [585, 466, 46]-code), using the BCH-code C(I) with length 585 | 163−1, defining interval I = {−4,−3,…,40}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(16113, 585, F16, 43) (dual of [585, 472, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 585 | 163−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(16125, 585, F16, 47) (dual of [585, 460, 48]-code), using the BCH-code C(I) with length 585 | 163−1, defining interval I = {−4,−3,…,42}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(16107, 585, F16, 41) (dual of [585, 478, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 585 | 163−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(163, 15, F16, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,16) or 15-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(161, 7, F16, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, 16, F16, 1) (dual of [16, 15, 2]-code), using
- Reed–Solomon code RS(15,16) [i]
- discarding factors / shortening the dual code based on linear OA(161, 16, F16, 1) (dual of [16, 15, 2]-code), 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(16129, 303, F16, 2, 47) (dual of [(303, 2), 477, 48]-NRT-code) | [i] | OOA Folding | |