Information on Result #714767
Linear OA(871, 96, F8, 40) (dual of [96, 25, 41]-code), using construction XX applied to C1 = C([53,26]), C2 = C([1,29]), C3 = C1 + C2 = C([1,26]), and C∩ = C1 ∩ C2 = C([53,29]) based on
- linear OA(850, 63, F8, 37) (dual of [63, 13, 38]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−10,−9,…,26}, and designed minimum distance d ≥ |I|+1 = 38 [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(855, 63, F8, 40) (dual of [63, 8, 41]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−10,−9,…,29}, and designed minimum distance d ≥ |I|+1 = 41 [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(814, 26, F8, 10) (dual of [26, 12, 11]-code), using
- construction X applied to AG(F,12P) ⊂ AG(F,14P) [i] based on
- linear OA(813, 23, F8, 10) (dual of [23, 10, 11]-code), using algebraic-geometric code AG(F,12P) [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- linear OA(811, 23, F8, 8) (dual of [23, 12, 9]-code), using algebraic-geometric code AG(F,14P) [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24 (see above)
- linear OA(81, 3, F8, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(813, 23, F8, 10) (dual of [23, 10, 11]-code), using algebraic-geometric code AG(F,12P) [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- construction X applied to AG(F,12P) ⊂ AG(F,14P) [i] based on
- 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(871, 48, F8, 2, 40) (dual of [(48, 2), 25, 41]-NRT-code) | [i] | OOA Folding | |