Information on Result #714636
Linear OA(858, 90, F8, 31) (dual of [90, 32, 32]-code), using construction XX applied to C1 = C([54,19]), C2 = C([0,21]), C3 = C1 + C2 = C([0,19]), and C∩ = C1 ∩ C2 = C([54,21]) based on
- linear OA(842, 63, F8, 29) (dual of [63, 21, 30]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−9,−8,…,19}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(835, 63, F8, 22) (dual of [63, 28, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [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 = {−9,−8,…,21}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(831, 63, F8, 20) (dual of [63, 32, 21]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(811, 22, F8, 8) (dual of [22, 11, 9]-code), using
- discarding factors / shortening the dual code based on 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, using
- the Klein quartic over F8 [i]
- algebraic-geometric code AG(F,14P) [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(811, 23, F8, 8) (dual of [23, 12, 9]-code), using
- linear OA(81, 5, F8, 1) (dual of [5, 4, 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(858, 45, F8, 2, 31) (dual of [(45, 2), 32, 32]-NRT-code) | [i] | OOA Folding | |