Information on Result #714617
Linear OA(856, 90, F8, 30) (dual of [90, 34, 31]-code), using construction XX applied to C1 = C([54,18]), C2 = C([0,20]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([54,20]) based on
- linear OA(840, 63, F8, 28) (dual of [63, 23, 29]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−9,−8,…,18}, 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(844, 63, F8, 30) (dual of [63, 19, 31]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−9,−8,…,20}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(829, 63, F8, 19) (dual of [63, 34, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [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(856, 45, F8, 2, 30) (dual of [(45, 2), 34, 31]-NRT-code) | [i] | OOA Folding | |