Information on Result #721493
Linear OA(1689, 116, F16, 56) (dual of [116, 27, 57]-code), using construction XX applied to C1 = C([1,50]), C2 = C([12,56]), C3 = C1 + C2 = C([12,50]), 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(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(1658, 85, F16, 39) (dual of [85, 27, 40]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {12,13,…,50}, and designed minimum distance d ≥ |I|+1 = 40 [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(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 OA(1688, 115, F16, 55) (dual of [115, 27, 56]-code) | [i] | Truncation | |
| 2 | Linear OA(1687, 114, F16, 54) (dual of [114, 27, 55]-code) | [i] | ||
| 3 | Linear OOA(1689, 58, F16, 2, 56) (dual of [(58, 2), 27, 57]-NRT-code) | [i] | OOA Folding | |