Information on Result #726885
Linear OA(27106, 786, F27, 45) (dual of [786, 680, 46]-code), using construction XX applied to C1 = C([721,27]), C2 = C([4,37]), C3 = C1 + C2 = C([4,27]), and C∩ = C1 ∩ C2 = C([721,37]) based on
- linear OA(2767, 728, F27, 35) (dual of [728, 661, 36]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−7,−6,…,27}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2767, 728, F27, 34) (dual of [728, 661, 35]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {4,5,…,37}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2786, 728, F27, 45) (dual of [728, 642, 46]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−7,−6,…,37}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(2748, 728, F27, 24) (dual of [728, 680, 25]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {4,5,…,27}, and designed minimum distance d ≥ |I|+1 = 25 [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(27106, 393, F27, 2, 45) (dual of [(393, 2), 680, 46]-NRT-code) | [i] | OOA Folding | |