Information on Result #678374
Linear OA(438, 262155, F4, 6) (dual of [262155, 262117, 7]-code), using construction X4 applied to Ce(5) ⊂ Ce(4) based on
- linear OA(437, 262144, F4, 6) (dual of [262144, 262107, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(428, 262144, F4, 5) (dual of [262144, 262116, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(410, 11, F4, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,4)), using
- dual of repetition code with length 11 [i]
- linear OA(41, 11, F4, 1) (dual of [11, 10, 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 OA(439, 262156, F4, 6) (dual of [262156, 262117, 7]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(438, 262155, F4, 2, 6) (dual of [(262155, 2), 524272, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(438, 262155, F4, 3, 6) (dual of [(262155, 3), 786427, 7]-NRT-code) | [i] | ||
| 4 | Digital (32, 38, 262155)-net over F4 | [i] | ||
| 5 | Linear OOA(438, 131077, F4, 2, 6) (dual of [(131077, 2), 262116, 7]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(438, 87385, F4, 3, 6) (dual of [(87385, 3), 262117, 7]-NRT-code) | [i] | ||
| 7 | Linear OOA(438, 87385, F4, 6, 6) (dual of [(87385, 6), 524272, 7]-NRT-code) | [i] | OA Folding and Stacking | |