Information on Result #1420193
Linear OOA(451, 65556, F4, 2, 8) (dual of [(65556, 2), 131061, 9]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(451, 65556, F4, 8) (dual of [65556, 65505, 9]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(450, 65554, F4, 8) (dual of [65554, 65504, 9]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(449, 65536, F4, 9) (dual of [65536, 65487, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- 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(417, 18, F4, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,4)), using
- dual of repetition code with length 18 [i]
- linear OA(41, 18, F4, 1) (dual of [18, 17, 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
- construction X4 applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(450, 65555, F4, 7) (dual of [65555, 65505, 8]-code), using Gilbert–Varšamov bound and bm = 450 > Vbs−1(k−1) = 80334 868316 187991 022541 334696 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 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
- linear OA(450, 65554, F4, 8) (dual of [65554, 65504, 9]-code), using
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(451, 32778, F4, 3, 8) (dual of [(32778, 3), 98283, 9]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(451, 32777, F4, 10, 8) (dual of [(32777, 10), 327719, 9]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |