Information on Result #691602
Linear OA(1678, 1048588, F16, 17) (dual of [1048588, 1048510, 18]-code), using construction X applied to Ce(16) ⊂ Ce(13) based on
- linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 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(162, 12, F16, 2) (dual of [12, 10, 3]-code or 12-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
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 OA(1677, 1048587, F16, 16) (dual of [1048587, 1048510, 17]-code) | [i] | Truncation | |
| 2 | Linear OOA(1678, 649860, F16, 2, 17) (dual of [(649860, 2), 1299642, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (61, 78, 649860)-net over F16 | [i] | ||
| 4 | Linear OOA(1678, 524294, F16, 2, 17) (dual of [(524294, 2), 1048510, 18]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(1678, 131073, F16, 17, 17) (dual of [(131073, 17), 2228163, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |