Information on Result #720489
Linear OA(9122, 762, F9, 42) (dual of [762, 640, 43]-code), using construction XX applied to C1 = C([52,91]), C2 = C([59,93]), C3 = C1 + C2 = C([59,91]), and C∩ = C1 ∩ C2 = C([52,93]) based on
- linear OA(9106, 728, F9, 40) (dual of [728, 622, 41]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {52,53,…,91}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(994, 728, F9, 35) (dual of [728, 634, 36]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {59,60,…,93}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(9112, 728, F9, 42) (dual of [728, 616, 43]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {52,53,…,93}, and designed minimum distance d ≥ |I|+1 = 43 [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 = {59,60,…,91}, and designed minimum distance d ≥ |I|+1 = 34 [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(91, 7, F9, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, 9, F9, 1) (dual of [9, 8, 2]-code), using
- Reed–Solomon code RS(8,9) [i]
- discarding factors / shortening the dual code based on linear OA(91, 9, F9, 1) (dual of [9, 8, 2]-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(9122, 381, F9, 2, 42) (dual of [(381, 2), 640, 43]-NRT-code) | [i] | OOA Folding | |