Information on Result #721500
Linear OA(1687, 112, F16, 56) (dual of [112, 25, 57]-code), using construction XX applied to C1 = C([1,50]), C2 = C([11,56]), C3 = C1 + C2 = C([11,50]), and C∩ = C1 ∩ C2 = C([1,56]) based on
- linear OA(1668, 85, F16, 50) (dual of [85, 17, 51]-code), using the narrow-sense BCH-code C(I) with length 85 | 162−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(1665, 85, F16, 46) (dual of [85, 20, 47]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {11,12,…,56}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(1673, 85, F16, 56) (dual of [85, 12, 57]-code), using the narrow-sense BCH-code C(I) with length 85 | 162−1, defining interval I = [1,56], and designed minimum distance d ≥ |I|+1 = 57 [i]
- linear OA(1660, 85, F16, 40) (dual of [85, 25, 41]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {11,12,…,50}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(169, 17, F16, 9) (dual of [17, 8, 10]-code or 17-arc in PG(8,16)), using
- extended Reed–Solomon code RSe(8,16) [i]
- the expurgated narrow-sense BCH-code C(I) with length 17 | 162−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(165, 10, F16, 5) (dual of [10, 5, 6]-code or 10-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
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(1687, 56, F16, 2, 56) (dual of [(56, 2), 25, 57]-NRT-code) | [i] | OOA Folding | |