Information on Result #714605
Linear OA(858, 94, F8, 30) (dual of [94, 36, 31]-code), using construction XX applied to C1 = C([54,17]), C2 = C([1,20]), C3 = C1 + C2 = C([1,17]), and C∩ = C1 ∩ C2 = C([54,20]) based on
- linear OA(839, 63, F8, 27) (dual of [63, 24, 28]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−9,−8,…,17}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(832, 63, F8, 20) (dual of [63, 31, 21]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(827, 63, F8, 17) (dual of [63, 36, 18]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(812, 24, F8, 9) (dual of [24, 12, 10]-code), using
- extended algebraic-geometric code AGe(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,7P) with degPÂ =Â 2 [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using the Klein quartic over F8 [i]
- extended algebraic-geometric code AGe(F,14P) [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- 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 OA(859, 95, F8, 30) (dual of [95, 36, 31]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(857, 93, F8, 29) (dual of [93, 36, 30]-code) | [i] | Truncation | |
| 3 | Linear OOA(858, 47, F8, 2, 30) (dual of [(47, 2), 36, 31]-NRT-code) | [i] | OOA Folding | |