Information on Result #1449367
Linear OOA(953, 1062900, F9, 2, 9) (dual of [(1062900, 2), 2125747, 10]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(953, 1062900, F9, 9) (dual of [1062900, 1062847, 10]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(952, 1062898, F9, 9) (dual of [1062898, 1062846, 10]-code), using
- trace code [i] based on linear OA(8126, 531449, F81, 9) (dual of [531449, 531423, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(8125, 531442, F81, 9) (dual of [531442, 531417, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(8119, 531442, F81, 7) (dual of [531442, 531423, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(811, 7, F81, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- trace code [i] based on linear OA(8126, 531449, F81, 9) (dual of [531449, 531423, 10]-code), using
- linear OA(952, 1062899, F9, 8) (dual of [1062899, 1062847, 9]-code), using Gilbert–Varšamov bound and bm = 952 > Vbs−1(k−1) = 637 723290 906687 576572 761467 733912 788063 173073 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(952, 1062898, F9, 9) (dual of [1062898, 1062846, 10]-code), using
Mode: 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(953, 531450, F9, 3, 9) (dual of [(531450, 3), 1594297, 10]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(953, 531449, F9, 10, 9) (dual of [(531449, 10), 5314437, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |