Information on Result #719137
Linear OA(962, 771, F9, 18) (dual of [771, 709, 19]-code), using construction XX applied to C1 = C([88,101]), C2 = C([84,94]), C3 = C1 + C2 = C([88,94]), and C∩ = C1 ∩ C2 = C([84,101]) based on
- linear OA(937, 728, F9, 14) (dual of [728, 691, 15]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {88,89,…,101}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(931, 728, F9, 11) (dual of [728, 697, 12]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {84,85,…,94}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(949, 728, F9, 18) (dual of [728, 679, 19]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {84,85,…,101}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(919, 728, F9, 7) (dual of [728, 709, 8]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {88,89,…,94}, and designed minimum distance d ≥ |I|+1 = 8 [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(94, 16, F9, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,9)), 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(962, 385, F9, 2, 18) (dual of [(385, 2), 708, 19]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(962, 257, F9, 3, 18) (dual of [(257, 3), 709, 19]-NRT-code) | [i] | ||