Information on Result #714799
Linear OA(875, 97, F8, 45) (dual of [97, 22, 46]-code), using construction XX applied to C1 = C([9,45]), C2 = C([1,35]), C3 = C1 + C2 = C([9,35]), and C∩ = C1 ∩ C2 = C([1,45]) based on
- linear OA(849, 63, F8, 37) (dual of [63, 14, 38]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {9,10,…,45}, and designed minimum distance d ≥ |I|+1 = 38 [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(855, 63, F8, 45) (dual of [63, 8, 46]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- 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 = {9,10,…,35}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(812, 20, F8, 9) (dual of [20, 8, 10]-code), using
- discarding factors / shortening the dual code 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]
- algebraic-geometric code AG(F,13P) [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(812, 23, F8, 9) (dual of [23, 11, 10]-code), using
- linear OA(88, 14, F8, 7) (dual of [14, 6, 8]-code), using
- extended algebraic-geometric code AGe(F,6P) [i] based on function field F/F8 with g(F) = 1 and N(F) ≥ 14, 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(876, 98, F8, 45) (dual of [98, 22, 46]-code) | [i] | Code Embedding in Larger Space | |