Information on Result #678646
Linear OA(434, 65546, F4, 6) (dual of [65546, 65512, 7]-code), using construction X4 applied to Ce(5) ⊂ Ce(4) based on
- linear OA(433, 65536, F4, 6) (dual of [65536, 65503, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(425, 65536, F4, 5) (dual of [65536, 65511, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(49, 10, F4, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,4)), using
- dual of repetition code with length 10 [i]
- linear OA(41, 10, F4, 1) (dual of [10, 9, 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(435, 65547, F4, 6) (dual of [65547, 65512, 7]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(434, 65546, F4, 2, 6) (dual of [(65546, 2), 131058, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(434, 65546, F4, 3, 6) (dual of [(65546, 3), 196604, 7]-NRT-code) | [i] | ||
| 4 | Digital (28, 34, 65546)-net over F4 | [i] | ||
| 5 | Linear OOA(434, 32773, F4, 2, 6) (dual of [(32773, 2), 65512, 7]-NRT-code) | [i] | OOA Folding | |