Information on Result #721375
Linear OA(1653, 100, F16, 30) (dual of [100, 47, 31]-code), using construction XX applied to C1 = C([79,22]), C2 = C([0,23]), C3 = C1 + C2 = C([0,22]), and C∩ = C1 ∩ C2 = C([79,23]) based on
- linear OA(1646, 85, F16, 29) (dual of [85, 39, 30]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {−6,−5,…,22}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(1640, 85, F16, 24) (dual of [85, 45, 25]-code), using the expurgated narrow-sense BCH-code C(I) with length 85 | 162−1, defining interval I = [0,23], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(1648, 85, F16, 30) (dual of [85, 37, 31]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {−6,−5,…,23}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(1638, 85, F16, 23) (dual of [85, 47, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 85 | 162−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(165, 13, F16, 5) (dual of [13, 8, 6]-code or 13-arc in PG(4,16)), using
- discarding factors / shortening the dual code based on linear OA(165, 16, F16, 5) (dual of [16, 11, 6]-code or 16-arc in PG(4,16)), using
- Reed–Solomon code RS(11,16) [i]
- discarding factors / shortening the dual code based on linear OA(165, 16, F16, 5) (dual of [16, 11, 6]-code or 16-arc in PG(4,16)), 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(1653, 50, F16, 2, 30) (dual of [(50, 2), 47, 31]-NRT-code) | [i] | OOA Folding | |