Information on Result #732117
Linear OA(1678, 1048668, F16, 14) (dual of [1048668, 1048590, 15]-code), using (u, u+v)-construction based on
- linear OA(1612, 87, F16, 7) (dual of [87, 75, 8]-code), using
- construction X applied to C([5,11]) ⊂ C([6,11]) [i] based on
- linear OA(1612, 85, F16, 7) (dual of [85, 73, 8]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {5,6,…,11}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(1610, 85, F16, 6) (dual of [85, 75, 7]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {6,7,…,11}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(160, 2, F16, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to C([5,11]) ⊂ C([6,11]) [i] based on
- linear OA(1666, 1048581, F16, 14) (dual of [1048581, 1048515, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(1666, 1048576, F16, 14) (dual of [1048576, 1048510, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(1661, 1048576, F16, 13) (dual of [1048576, 1048515, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(160, 5, F16, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)
- construction X applied to Ce(13) ⊂ Ce(12) [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(1678, 524334, F16, 2, 14) (dual of [(524334, 2), 1048590, 15]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(1678, 149809, F16, 14, 14) (dual of [(149809, 14), 2097248, 15]-NRT-code) | [i] | OA Folding and Stacking | |