Information on Result #1307700
Linear OA(469, 534, F4, 19) (dual of [534, 465, 20]-code), using 17 step Varšamov–Edel lengthening with (ri) = (1, 16 times 0) based on linear OA(468, 516, F4, 19) (dual of [516, 448, 20]-code), using
- trace code [i] based on linear OA(1634, 258, F16, 19) (dual of [258, 224, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(1634, 256, F16, 19) (dual of [256, 222, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(1632, 256, F16, 18) (dual of [256, 224, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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 Ce(18) ⊂ Ce(17) [i] based on
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(469, 534, F4, 2, 19) (dual of [(534, 2), 999, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(469, 534, F4, 3, 19) (dual of [(534, 3), 1533, 20]-NRT-code) | [i] | ||
| 3 | Digital (50, 69, 534)-net over F4 | [i] | ||