Information on Result #822766
Linear OOA(472, 524294, F4, 2, 10) (dual of [(524294, 2), 1048516, 11]-NRT-code), using OOA 2-folding based on linear OA(472, 1048588, F4, 10) (dual of [1048588, 1048516, 11]-code), using
- construction X4 applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(471, 1048576, F4, 10) (dual of [1048576, 1048505, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(461, 1048576, F4, 9) (dual of [1048576, 1048515, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(411, 12, F4, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,4)), using
- dual of repetition code with length 12 [i]
- linear OA(41, 12, F4, 1) (dual of [12, 11, 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(473, 524294, F4, 2, 10) (dual of [(524294, 2), 1048515, 11]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(472, 524294, F4, 3, 10) (dual of [(524294, 3), 1572810, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (62, 72, 524294)-net over F4 | [i] | ||