Information on Result #719218
Linear OA(963, 763, F9, 20) (dual of [763, 700, 21]-code), using construction XX applied to C1 = C([84,100]), C2 = C([81,93]), C3 = C1 + C2 = C([84,93]), and C∩ = C1 ∩ C2 = C([81,100]) based on
- linear OA(946, 728, F9, 17) (dual of [728, 682, 18]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {84,85,…,100}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(934, 728, F9, 13) (dual of [728, 694, 14]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {81,82,…,93}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(952, 728, F9, 20) (dual of [728, 676, 21]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {81,82,…,100}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(928, 728, F9, 10) (dual of [728, 700, 11]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {84,85,…,93}, and designed minimum distance d ≥ |I|+1 = 11 [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(92, 8, F9, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,9)), using
- discarding factors / shortening the dual code based on linear OA(92, 9, F9, 2) (dual of [9, 7, 3]-code or 9-arc in PG(1,9)), using
- Reed–Solomon code RS(7,9) [i]
- discarding factors / shortening the dual code based on linear OA(92, 9, F9, 2) (dual of [9, 7, 3]-code or 9-arc in PG(1,9)), 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(963, 381, F9, 2, 20) (dual of [(381, 2), 699, 21]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(963, 254, F9, 3, 20) (dual of [(254, 3), 699, 21]-NRT-code) | [i] | ||