Information on Result #701587
Linear OA(879, 86, F8, 63) (dual of [86, 7, 64]-code), using construction X applied to C([0,42]) ⊂ C({1,2,3,4,5,6,7,9,11,12,13,14,17,18,25,26,27,33,34,35,36,42}) based on
- linear OA(870, 73, F8, 63) (dual of [73, 3, 64]-code), using the expurgated narrow-sense BCH-code C(I) with length 73 | 83−1, defining interval I = [0,42], and minimum distance d ≥ |{−20,−19,…,42}|+1 = 64 (BCH-bound) [i]
- linear OA(866, 73, F8, 54) (dual of [73, 7, 55]-code), using the cyclic code C(A) with length 73 | 83−1, defining set A = {1,2,3,4,5,6,7,9,11,12,13,14,17,18,25,26,27,33,34,35,36,42}, and minimum distance d ≥ |{−9,12,33,…,9}|+1 = 55 (BCH-bound) [i]
- linear OA(89, 13, F8, 8) (dual of [13, 4, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(89, 14, F8, 8) (dual of [14, 5, 9]-code), using
- extended algebraic-geometric code AGe(F,5P) [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(89, 14, F8, 8) (dual of [14, 5, 9]-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 OA(879, 86, F8, 62) (dual of [86, 7, 63]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(879, 86, F8, 61) (dual of [86, 7, 62]-code) | [i] | ||
| 3 | Linear OA(8102, 109, F8, 77) (dual of [109, 7, 78]-code) | [i] | Juxtaposition | |
| 4 | Linear OA(8103, 110, F8, 78) (dual of [110, 7, 79]-code) | [i] | ||
| 5 | Linear OA(8142, 149, F8, 110) (dual of [149, 7, 111]-code) | [i] | ||
| 6 | Linear OOA(879, 43, F8, 2, 63) (dual of [(43, 2), 7, 64]-NRT-code) | [i] | OOA Folding | |