Information on Result #726854
Linear OA(2799, 774, F27, 44) (dual of [774, 675, 45]-code), using construction XX applied to C1 = C([718,27]), C2 = C([0,33]), C3 = C1 + C2 = C([0,27]), and C∩ = C1 ∩ C2 = C([718,33]) based on
- linear OA(2773, 728, F27, 38) (dual of [728, 655, 39]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−10,−9,…,27}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2764, 728, F27, 34) (dual of [728, 664, 35]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,33], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2784, 728, F27, 44) (dual of [728, 644, 45]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−10,−9,…,33}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(2753, 728, F27, 28) (dual of [728, 675, 29]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2710, 30, F27, 9) (dual of [30, 20, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(2710, 38, F27, 9) (dual of [38, 28, 10]-code), using
- extended algebraic-geometric code AGe(F,28P) [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(2710, 38, F27, 9) (dual of [38, 28, 10]-code), using
- linear OA(275, 16, F27, 5) (dual of [16, 11, 6]-code or 16-arc in PG(4,27)), using
- discarding factors / shortening the dual code based on linear OA(275, 27, F27, 5) (dual of [27, 22, 6]-code or 27-arc in PG(4,27)), using
- Reed–Solomon code RS(22,27) [i]
- discarding factors / shortening the dual code based on linear OA(275, 27, F27, 5) (dual of [27, 22, 6]-code or 27-arc in PG(4,27)), 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(2799, 387, F27, 2, 44) (dual of [(387, 2), 675, 45]-NRT-code) | [i] | OOA Folding | |