Information on Result #678419
Linear OA(4200, 262173, F4, 28) (dual of [262173, 261973, 29]-code), using construction X4 applied to Ce(29) ⊂ Ce(25) based on
- linear OA(4199, 262144, F4, 30) (dual of [262144, 261945, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4172, 262144, F4, 26) (dual of [262144, 261972, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(428, 29, F4, 28) (dual of [29, 1, 29]-code or 29-arc in PG(27,4)), using
- dual of repetition code with length 29 [i]
- linear OA(41, 29, F4, 1) (dual of [29, 28, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 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 OOA(4200, 142621, F4, 2, 28) (dual of [(142621, 2), 285042, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4200, 142621, F4, 3, 28) (dual of [(142621, 3), 427663, 29]-NRT-code) | [i] | ||
| 3 | Digital (172, 200, 142621)-net over F4 | [i] | ||