Information on Result #726941
Linear OA(27109, 788, F27, 46) (dual of [788, 679, 47]-code), using construction XX applied to C1 = C([721,28]), C2 = C([4,38]), C3 = C1 + C2 = C([4,28]), and C∩ = C1 ∩ C2 = C([721,38]) based on
- linear OA(2768, 728, F27, 36) (dual of [728, 660, 37]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−7,−6,…,28}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2769, 728, F27, 35) (dual of [728, 659, 36]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {4,5,…,38}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2788, 728, F27, 46) (dual of [728, 640, 47]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−7,−6,…,38}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(2749, 728, F27, 25) (dual of [728, 679, 26]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {4,5,…,28}, and designed minimum distance d ≥ |I|+1 = 26 [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(27110, 789, F27, 46) (dual of [789, 679, 47]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(27109, 394, F27, 2, 46) (dual of [(394, 2), 679, 47]-NRT-code) | [i] | OOA Folding | |