Information on Result #720428
Linear OA(9127, 782, F9, 41) (dual of [782, 655, 42]-code), using construction XX applied to C1 = C([67,100]), C2 = C([60,93]), C3 = C1 + C2 = C([67,93]), and C∩ = C1 ∩ C2 = C([60,100]) based on
- linear OA(991, 728, F9, 34) (dual of [728, 637, 35]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {67,68,…,100}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(991, 728, F9, 34) (dual of [728, 637, 35]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {60,61,…,93}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(9109, 728, F9, 41) (dual of [728, 619, 42]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {60,61,…,100}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(973, 728, F9, 27) (dual of [728, 655, 28]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {67,68,…,93}, and designed minimum distance d ≥ |I|+1 = 28 [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(9127, 391, F9, 2, 41) (dual of [(391, 2), 655, 42]-NRT-code) | [i] | OOA Folding | |