Information on Result #731850
Linear OA(440, 16408, F4, 7) (dual of [16408, 16368, 8]-code), using (u, u+v)-construction based on
- linear OA(44, 17, F4, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
- linear OA(436, 16391, F4, 7) (dual of [16391, 16355, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(436, 16384, F4, 7) (dual of [16384, 16348, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(429, 16384, F4, 6) (dual of [16384, 16355, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(40, 7, F4, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
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(440, 16408, F4, 2, 7) (dual of [(16408, 2), 32776, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(440, 16408, F4, 3, 7) (dual of [(16408, 3), 49184, 8]-NRT-code) | [i] | ||
| 3 | Digital (33, 40, 16408)-net over F4 | [i] | ||
| 4 | Linear OOA(440, 8204, F4, 2, 7) (dual of [(8204, 2), 16368, 8]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(440, 5469, F4, 3, 7) (dual of [(5469, 3), 16367, 8]-NRT-code) | [i] | ||