Information on Result #714837
Linear OA(874, 90, F8, 48) (dual of [90, 16, 49]-code), using construction XX applied to C1 = C([53,35]), C2 = C([1,37]), C3 = C1 + C2 = C([1,35]), and C∩ = C1 ∩ C2 = C([53,37]) based on
- linear OA(857, 63, F8, 46) (dual of [63, 6, 47]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−10,−9,…,35}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(850, 63, F8, 37) (dual of [63, 13, 38]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(860, 63, F8, 48) (dual of [63, 3, 49]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−10,−9,…,37}, and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(847, 63, F8, 35) (dual of [63, 16, 36]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- 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]
- algebraic-geometric code AG(F,12P) [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- linear OA(81, 4, F8, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-code), using
- Reed–Solomon code RS(7,8) [i]
- discarding factors / shortening the dual code based on linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-code), 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(874, 45, F8, 2, 48) (dual of [(45, 2), 16, 49]-NRT-code) | [i] | OOA Folding | |