Information on Result #726607
Linear OA(2797, 788, F27, 40) (dual of [788, 691, 41]-code), using construction XX applied to C1 = C([727,28]), C2 = C([10,38]), C3 = C1 + C2 = C([10,28]), and C∩ = C1 ∩ C2 = C([727,38]) based on
- linear OA(2756, 728, F27, 30) (dual of [728, 672, 31]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,28}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2757, 728, F27, 29) (dual of [728, 671, 30]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {10,11,…,38}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2776, 728, F27, 40) (dual of [728, 652, 41]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,38}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2737, 728, F27, 19) (dual of [728, 691, 20]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {10,11,…,28}, and designed minimum distance d ≥ |I|+1 = 20 [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(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 (see above)
- discarding factors / shortening the dual code based on linear OA(2710, 38, F27, 9) (dual of [38, 28, 10]-code), 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 OA(2798, 789, F27, 40) (dual of [789, 691, 41]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2799, 790, F27, 40) (dual of [790, 691, 41]-code) | [i] | ||
| 3 | Linear OOA(2797, 394, F27, 2, 40) (dual of [(394, 2), 691, 41]-NRT-code) | [i] | OOA Folding | |