Information on Result #714822
Linear OA(876, 96, F8, 46) (dual of [96, 20, 47]-code), using construction XX applied to C1 = C([8,45]), C2 = C([0,35]), C3 = C1 + C2 = C([8,35]), and C∩ = C1 ∩ C2 = C([0,45]) based on
- linear OA(851, 63, F8, 38) (dual of [63, 12, 39]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {8,9,…,45}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(848, 63, F8, 36) (dual of [63, 15, 37]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,35], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(856, 63, F8, 46) (dual of [63, 7, 47]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,45], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(841, 63, F8, 28) (dual of [63, 22, 29]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {8,9,…,35}, and designed minimum distance d ≥ |I|+1 = 29 [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, 13, F8, 7) (dual of [13, 5, 8]-code), using
- discarding factors / shortening the dual code based on 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
- discarding factors / shortening the dual code based on linear OA(88, 14, F8, 7) (dual of [14, 6, 8]-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(876, 48, F8, 2, 46) (dual of [(48, 2), 20, 47]-NRT-code) | [i] | OOA Folding | |