Information on Result #1299727
Linear OA(435, 65548, F4, 6) (dual of [65548, 65513, 7]-code), using construction X with Varšamov bound based on
- linear OA(433, 65544, F4, 6) (dual of [65544, 65511, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] 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(40, 8, F4, 0) (dual of [8, 8, 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(433, 65546, F4, 5) (dual of [65546, 65513, 6]-code), using Gilbert–Varšamov bound and bm = 433 > Vbs−1(k−1) = 62 287532 567164 613146 [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(435, 65548, F4, 2, 6) (dual of [(65548, 2), 131061, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(435, 65548, F4, 3, 6) (dual of [(65548, 3), 196609, 7]-NRT-code) | [i] | ||
| 3 | Digital (29, 35, 65548)-net over F4 | [i] | ||
| 4 | Linear OOA(435, 32774, F4, 2, 6) (dual of [(32774, 2), 65513, 7]-NRT-code) | [i] | OOA Folding | |