Information on Result #714774
Linear OA(864, 86, F8, 39) (dual of [86, 22, 40]-code), using construction XX applied to C1 = C([10,45]), C2 = C([7,37]), C3 = C1 + C2 = C([10,37]), and C∩ = C1 ∩ C2 = C([7,45]) based on
- linear OA(848, 63, F8, 36) (dual of [63, 15, 37]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {10,11,…,45}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(846, 63, F8, 31) (dual of [63, 17, 32]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {7,8,…,37}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(853, 63, F8, 39) (dual of [63, 10, 40]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {7,8,…,45}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(841, 63, F8, 28) (dual of [63, 22, 29]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {10,11,…,37}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(89, 16, F8, 7) (dual of [16, 7, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(89, 17, F8, 7) (dual of [17, 8, 8]-code), using
- extended algebraic-geometric code AGe(F,9P) [i] based on function field F/F8 with g(F) = 2 and N(F) ≥ 17, using
- discarding factors / shortening the dual code based on linear OA(89, 17, F8, 7) (dual of [17, 8, 8]-code), using
- linear OA(82, 7, F8, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,8)), using
- discarding factors / shortening the dual code based on linear OA(82, 8, F8, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,8)), using
- Reed–Solomon code RS(6,8) [i]
- discarding factors / shortening the dual code based on linear OA(82, 8, F8, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,8)), 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(864, 43, F8, 2, 39) (dual of [(43, 2), 22, 40]-NRT-code) | [i] | OOA Folding | |