Information on Result #726138
Linear OA(2776, 768, F27, 33) (dual of [768, 692, 34]-code), using construction XX applied to C1 = C([727,27]), C2 = C([10,31]), C3 = C1 + C2 = C([10,27]), and C∩ = C1 ∩ C2 = C([727,31]) 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(2743, 728, F27, 22) (dual of [728, 685, 23]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {10,11,…,31}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2762, 728, F27, 33) (dual of [728, 666, 34]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,31}, and designed minimum distance d ≥ |I|+1 = 34 [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(273, 10, F27, 3) (dual of [10, 7, 4]-code or 10-arc in PG(2,27) or 10-cap in PG(2,27)), using
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- Reed–Solomon code RS(24,27) [i]
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), 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(2776, 384, F27, 2, 33) (dual of [(384, 2), 692, 34]-NRT-code) | [i] | OOA Folding | |