Information on Result #714615
Linear OA(861, 96, F8, 31) (dual of [96, 35, 32]-code), using construction XX applied to C1 = C([53,17]), C2 = C([0,20]), C3 = C1 + C2 = C([0,17]), and C∩ = C1 ∩ C2 = C([53,20]) based on
- 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,−9,…,17}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(833, 63, F8, 21) (dual of [63, 30, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [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 = {−10,−9,…,20}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(828, 63, F8, 18) (dual of [63, 35, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(813, 26, F8, 9) (dual of [26, 13, 10]-code), using
- construction X applied to AG(F,13P) ⊂ AG(F,15P) [i] 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]
- linear OA(810, 23, F8, 7) (dual of [23, 13, 8]-code), using algebraic-geometric code AG(F,15P) [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(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
- construction X applied to AG(F,13P) ⊂ AG(F,15P) [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(861, 48, F8, 2, 31) (dual of [(48, 2), 35, 32]-NRT-code) | [i] | OOA Folding | |