Information on Result #1454970
Linear OOA(16114, 923750, F16, 2, 24) (dual of [(923750, 2), 1847386, 25]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(16114, 923750, F16, 24) (dual of [923750, 923636, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(16114, 1048594, F16, 24) (dual of [1048594, 1048480, 25]-code), using
- 1 times code embedding in larger space [i] based on linear OA(16113, 1048593, F16, 24) (dual of [1048593, 1048480, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- linear OA(16111, 1048576, F16, 24) (dual of [1048576, 1048465, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(1696, 1048576, F16, 21) (dual of [1048576, 1048480, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(162, 17, F16, 2) (dual of [17, 15, 3]-code or 17-arc in PG(1,16)), using
- extended Reed–Solomon code RSe(15,16) [i]
- Hamming code H(2,16) [i]
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(16113, 1048593, F16, 24) (dual of [1048593, 1048480, 25]-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(16114, 153958, F16, 26, 24) (dual of [(153958, 26), 4002794, 25]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |