Information on Result #720258
Linear OA(9109, 758, F9, 38) (dual of [758, 649, 39]-code), using construction XX applied to C1 = C([55,91]), C2 = C([62,92]), C3 = C1 + C2 = C([62,91]), and C∩ = C1 ∩ C2 = C([55,92]) based on
- linear OA(997, 728, F9, 37) (dual of [728, 631, 38]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {55,56,…,91}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(982, 728, F9, 31) (dual of [728, 646, 32]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {62,63,…,92}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(9100, 728, F9, 38) (dual of [728, 628, 39]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {55,56,…,92}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(979, 728, F9, 30) (dual of [728, 649, 31]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {62,63,…,91}, 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(90, 3, F9, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(9109, 379, F9, 2, 38) (dual of [(379, 2), 649, 39]-NRT-code) | [i] | OOA Folding | |