Information on Result #726665
Linear OA(2798, 786, F27, 41) (dual of [786, 688, 42]-code), using construction XX applied to C1 = C([725,27]), C2 = C([8,37]), C3 = C1 + C2 = C([8,27]), and C∩ = C1 ∩ C2 = C([725,37]) based on
- linear OA(2759, 728, F27, 31) (dual of [728, 669, 32]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−3,−2,…,27}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2759, 728, F27, 30) (dual of [728, 669, 31]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {8,9,…,37}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2778, 728, F27, 41) (dual of [728, 650, 42]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−3,−2,…,37}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2740, 728, F27, 20) (dual of [728, 688, 21]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {8,9,…,27}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2711, 30, F27, 10) (dual of [30, 19, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2711, 38, F27, 10) (dual of [38, 27, 11]-code), using
- extended algebraic-geometric code AGe(F,27P) [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- discarding factors / shortening the dual code based on linear OA(2711, 38, F27, 10) (dual of [38, 27, 11]-code), using
- linear OA(279, 28, F27, 9) (dual of [28, 19, 10]-code or 28-arc in PG(8,27)), using
- extended Reed–Solomon code RSe(19,27) [i]
- the expurgated narrow-sense BCH-code C(I) with length 28 | 272−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
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(2798, 393, F27, 2, 41) (dual of [(393, 2), 688, 42]-NRT-code) | [i] | OOA Folding | |