Information on Result #720494
Linear OA(9136, 789, F9, 43) (dual of [789, 653, 44]-code), using construction XX applied to C1 = C([55,90]), C2 = C([63,97]), C3 = C1 + C2 = C([63,90]), and C∩ = C1 ∩ C2 = C([55,97]) based on
- linear OA(996, 728, F9, 36) (dual of [728, 632, 37]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {55,56,…,90}, and designed minimum distance d ≥ |I|+1 = 37 [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 = {63,64,…,97}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(9115, 728, F9, 43) (dual of [728, 613, 44]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {55,56,…,97}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(975, 728, F9, 28) (dual of [728, 653, 29]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {63,64,…,90}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(912, 33, F9, 7) (dual of [33, 21, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(912, 40, F9, 7) (dual of [40, 28, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 40 | 92−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(912, 40, F9, 7) (dual of [40, 28, 8]-code), using
- 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
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 OA(9138, 791, F9, 43) (dual of [791, 653, 44]-code) | [i] | Code Embedding in Larger Space | |