Information on Result #691600
Linear OA(1687, 1048587, F16, 19) (dual of [1048587, 1048500, 20]-code), using construction X applied to Ce(18) ⊂ Ce(16) based on
- linear OA(1686, 1048576, F16, 19) (dual of [1048576, 1048490, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 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(161, 11, F16, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(1688, 1048588, F16, 19) (dual of [1048588, 1048500, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(16100, 1048632, F16, 19) (dual of [1048632, 1048532, 20]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OOA(1687, 590579, F16, 2, 19) (dual of [(590579, 2), 1181071, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (68, 87, 590579)-net over F16 | [i] | ||
| 5 | Linear OOA(1687, 524293, F16, 2, 19) (dual of [(524293, 2), 1048499, 20]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(1687, 116509, F16, 19, 19) (dual of [(116509, 19), 2213584, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |