Information on Result #721495
Linear OA(1688, 114, F16, 56) (dual of [114, 26, 57]-code), using construction XX applied to C1 = C([1,51]), C2 = C([12,56]), C3 = C1 + C2 = C([12,51]), and C∩ = C1 ∩ C2 = C([1,56]) based on
- linear OA(1669, 85, F16, 51) (dual of [85, 16, 52]-code), using the narrow-sense BCH-code C(I) with length 85 | 162−1, defining interval I = [1,51], and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(1663, 85, F16, 45) (dual of [85, 22, 46]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {12,13,…,56}, and designed minimum distance d ≥ |I|+1 = 46 [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(1659, 85, F16, 40) (dual of [85, 26, 41]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {12,13,…,51}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(1611, 21, F16, 10) (dual of [21, 10, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(1611, 24, F16, 10) (dual of [24, 13, 11]-code), using
- extended algebraic-geometric code AGe(F,13P) [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(1611, 24, F16, 10) (dual of [24, 13, 11]-code), using
- linear OA(164, 8, F16, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,16)), using
- discarding factors / shortening the dual code based on linear OA(164, 16, F16, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,16)), using
- Reed–Solomon code RS(12,16) [i]
- discarding factors / shortening the dual code based on linear OA(164, 16, F16, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,16)), 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(1688, 57, F16, 2, 56) (dual of [(57, 2), 26, 57]-NRT-code) | [i] | OOA Folding | |