Information on Result #719780
Linear OA(997, 782, F9, 30) (dual of [782, 685, 31]-code), using construction XX applied to C1 = C([78,100]), C2 = C([71,93]), C3 = C1 + C2 = C([78,93]), and C∩ = C1 ∩ C2 = C([71,100]) based on
- linear OA(961, 728, F9, 23) (dual of [728, 667, 24]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {78,79,…,100}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(961, 728, F9, 23) (dual of [728, 667, 24]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {71,72,…,93}, and designed minimum distance d ≥ |I|+1 = 24 [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 = {71,72,…,100}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(943, 728, F9, 16) (dual of [728, 685, 17]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {78,79,…,93}, and designed minimum distance d ≥ |I|+1 = 17 [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(99, 27, F9, 6) (dual of [27, 18, 7]-code) (see above)
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(997, 391, F9, 2, 30) (dual of [(391, 2), 685, 31]-NRT-code) | [i] | OOA Folding | |