Information on Result #714764
Linear OA(867, 92, F8, 39) (dual of [92, 25, 40]-code), using construction XX applied to C1 = C([54,26]), C2 = C([1,29]), C3 = C1 + C2 = C([1,26]), and C∩ = C1 ∩ C2 = C([54,29]) 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 = {−9,−8,…,26}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(843, 63, F8, 29) (dual of [63, 20, 30]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [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 = {−9,−8,…,29}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(838, 63, F8, 26) (dual of [63, 25, 27]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(812, 22, F8, 9) (dual of [22, 10, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(812, 23, F8, 9) (dual of [23, 11, 10]-code), using
- algebraic-geometric code AG(F,13P) [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- algebraic-geometric code AG(F,13P) [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- discarding factors / shortening the dual code based on linear OA(812, 23, F8, 9) (dual of [23, 11, 10]-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 OA(869, 94, F8, 39) (dual of [94, 25, 40]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(866, 91, F8, 38) (dual of [91, 25, 39]-code) | [i] | Truncation | |
| 3 | Linear OOA(867, 46, F8, 2, 39) (dual of [(46, 2), 25, 40]-NRT-code) | [i] | OOA Folding | |