Information on Result #714706
Linear OA(869, 102, F8, 36) (dual of [102, 33, 37]-code), using construction XX applied to C1 = C([9,36]), C2 = C([1,26]), C3 = C1 + C2 = C([9,26]), and C∩ = C1 ∩ C2 = C([1,36]) 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 = {9,10,…,36}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(838, 63, F8, 26) (dual of [63, 25, 27]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(848, 63, F8, 36) (dual of [63, 15, 37]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(828, 63, F8, 18) (dual of [63, 35, 19]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {9,10,…,26}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(812, 22, F8, 9) (dual of [22, 10, 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(89, 17, F8, 7) (dual of [17, 8, 8]-code), using
- extended algebraic-geometric code AGe(F,9P) [i] based on function field F/F8 with g(F) = 2 and N(F) ≥ 17, 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(869, 51, F8, 2, 36) (dual of [(51, 2), 33, 37]-NRT-code) | [i] | OOA Folding | |