Information on Result #720904
Linear OA(9146, 771, F9, 50) (dual of [771, 625, 51]-code), using construction XX applied to C1 = C([55,100]), C2 = C([51,93]), C3 = C1 + C2 = C([55,93]), and C∩ = C1 ∩ C2 = C([51,100]) based on
- linear OA(9121, 728, F9, 46) (dual of [728, 607, 47]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {55,56,…,100}, and designed minimum distance d ≥ |I|+1 = 47 [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 = {51,52,…,93}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(9133, 728, F9, 50) (dual of [728, 595, 51]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {51,52,…,100}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(9103, 728, F9, 39) (dual of [728, 625, 40]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {55,56,…,93}, and designed minimum distance d ≥ |I|+1 = 40 [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(9146, 385, F9, 2, 50) (dual of [(385, 2), 624, 51]-NRT-code) | [i] | OOA Folding |