Information on Result #726534
Linear OA(2794, 786, F27, 39) (dual of [786, 692, 40]-code), using construction XX applied to C1 = C([727,27]), C2 = C([10,37]), C3 = C1 + C2 = C([10,27]), and C∩ = C1 ∩ C2 = C([727,37]) based on
- linear OA(2755, 728, F27, 29) (dual of [728, 673, 30]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,27}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2755, 728, F27, 28) (dual of [728, 673, 29]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {10,11,…,37}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2774, 728, F27, 39) (dual of [728, 654, 40]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,37}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2736, 728, F27, 18) (dual of [728, 692, 19]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {10,11,…,27}, and designed minimum distance d ≥ |I|+1 = 19 [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(2794, 393, F27, 2, 39) (dual of [(393, 2), 692, 40]-NRT-code) | [i] | OOA Folding | |