Information on Result #1082426
Linear OOA(8155, 2362874, F81, 4, 11) (dual of [(2362874, 4), 9451441, 12]-NRT-code), using (u, u+v)-construction based on
- linear OOA(8114, 265724, F81, 4, 5) (dual of [(265724, 4), 1062882, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(8114, 531449, F81, 5) (dual of [531449, 531435, 6]-code), using
- construction X applied to C([0,2]) ⊂ C([0,1]) [i] based on
- linear OA(8113, 531442, F81, 5) (dual of [531442, 531429, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(817, 531442, F81, 3) (dual of [531442, 531435, 4]-code or 531442-cap in PG(6,81)), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,1], and minimum distance d ≥ |{−1,0,1}|+1 = 4 (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([0,2]) ⊂ C([0,1]) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(8114, 531449, F81, 5) (dual of [531449, 531435, 6]-code), using
- linear OOA(8141, 2097150, F81, 4, 11) (dual of [(2097150, 4), 8388559, 12]-NRT-code), using
- OOA 4-folding [i] based on linear OA(8141, 8388600, F81, 11) (dual of [8388600, 8388559, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(8141, large, F81, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8141, large, F81, 11) (dual of [large, large−41, 12]-code), using
- OOA 4-folding [i] based on linear OA(8141, 8388600, F81, 11) (dual of [8388600, 8388559, 12]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(8172, 4725748, F81, 4, 11) (dual of [(4725748, 4), 18902920, 12]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |