Information on Result #876426
Linear OOA(8138, 265724, F81, 2, 13) (dual of [(265724, 2), 531410, 14]-NRT-code), using OOA 2-folding based on linear OA(8138, 531448, F81, 13) (dual of [531448, 531410, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(8138, 531449, F81, 13) (dual of [531449, 531411, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- linear OA(8137, 531442, F81, 13) (dual of [531442, 531405, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(8131, 531442, F81, 11) (dual of [531442, 531411, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (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([0,6]) ⊂ C([0,5]) [i] based on
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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(8138, 265724, F81, 3, 13) (dual of [(265724, 3), 797134, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8138, 265724, F81, 4, 13) (dual of [(265724, 4), 1062858, 14]-NRT-code) | [i] | ||
| 3 | Digital (25, 38, 265724)-net over F81 | [i] | ||