Information on Result #719944
Linear OA(9104, 778, F9, 33) (dual of [778, 674, 34]-code), using construction XX applied to C1 = C([64,90]), C2 = C([71,96]), C3 = C1 + C2 = C([71,90]), and C∩ = C1 ∩ C2 = C([64,96]) based on
- linear OA(972, 728, F9, 27) (dual of [728, 656, 28]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {64,65,…,90}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(970, 728, F9, 26) (dual of [728, 658, 27]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {71,72,…,96}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(988, 728, F9, 33) (dual of [728, 640, 34]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {64,65,…,96}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(954, 728, F9, 20) (dual of [728, 674, 21]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {71,72,…,90}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(99, 27, F9, 6) (dual of [27, 18, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(99, 28, F9, 6) (dual of [28, 19, 7]-code), using
- extended algebraic-geometric code AGe(F,21P) [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- extended algebraic-geometric code AGe(F,21P) [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- discarding factors / shortening the dual code based on linear OA(99, 28, F9, 6) (dual of [28, 19, 7]-code), using
- linear OA(97, 23, F9, 5) (dual of [23, 16, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-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 OOA(9104, 389, F9, 2, 33) (dual of [(389, 2), 674, 34]-NRT-code) | [i] | OOA Folding | |