Information on Result #721468
Linear OA(1685, 118, F16, 51) (dual of [118, 33, 52]-code), using construction XX applied to C1 = C([12,56]), C2 = C([6,45]), C3 = C1 + C2 = C([12,45]), and C∩ = C1 ∩ C2 = C([6,56]) based on
- 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(1658, 85, F16, 40) (dual of [85, 27, 41]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {6,7,…,45}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(1669, 85, F16, 51) (dual of [85, 16, 52]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {6,7,…,56}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(1652, 85, F16, 34) (dual of [85, 33, 35]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {12,13,…,45}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(1611, 22, F16, 10) (dual of [22, 11, 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(165, 11, F16, 5) (dual of [11, 6, 6]-code or 11-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 OA(1685, 118, F16, 50) (dual of [118, 33, 51]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(1684, 117, F16, 50) (dual of [117, 33, 51]-code) | [i] | Truncation | |
| 3 | Linear OA(1683, 116, F16, 49) (dual of [116, 33, 50]-code) | [i] | ||
| 4 | Linear OOA(1685, 59, F16, 2, 51) (dual of [(59, 2), 33, 52]-NRT-code) | [i] | OOA Folding | |