Information on Result #1299784
Linear OA(447, 4194319, F4, 6) (dual of [4194319, 4194272, 7]-code), using construction X with Varšamov bound based on
- linear OA(445, 4194315, F4, 6) (dual of [4194315, 4194270, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(445, 4194304, F4, 6) (dual of [4194304, 4194259, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(434, 4194304, F4, 5) (dual of [4194304, 4194270, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(40, 11, F4, 0) (dual of [11, 11, 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(5) ⊂ Ce(4) [i] based on
- linear OA(445, 4194317, F4, 5) (dual of [4194317, 4194272, 6]-code), using Gilbert–Varšamov bound and bm = 445 > Vbs−1(k−1) = 1044 522699 534141 624369 067594 [i]
- linear OA(40, 2, F4, 0) (dual of [2, 2, 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 (see above)
Mode: 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(447, 4194319, F4, 2, 6) (dual of [(4194319, 2), 8388591, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(447, 4194319, F4, 3, 6) (dual of [(4194319, 3), 12582910, 7]-NRT-code) | [i] | ||
| 3 | Digital (41, 47, 4194319)-net over F4 | [i] | ||