Information on Result #720375
Linear OA(9117, 764, F9, 40) (dual of [764, 647, 41]-code), using construction XX applied to C1 = C([54,90]), C2 = C([61,93]), C3 = C1 + C2 = C([61,90]), and C∩ = C1 ∩ C2 = C([54,93]) based on
- linear OA(999, 728, F9, 37) (dual of [728, 629, 38]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {54,55,…,90}, and designed minimum distance d ≥ |I|+1 = 38 [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 = {61,62,…,93}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- 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 = {54,55,…,93}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(981, 728, F9, 30) (dual of [728, 647, 31]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {61,62,…,90}, and designed minimum distance d ≥ |I|+1 = 31 [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, 9, F9, 2) (dual of [9, 7, 3]-code or 9-arc in PG(1,9)), using
- Reed–Solomon code RS(7,9) [i]
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(9117, 382, F9, 2, 40) (dual of [(382, 2), 647, 41]-NRT-code) | [i] | OOA Folding | |