Information on Result #1420087
Linear OOA(444, 65558, F4, 2, 7) (dual of [(65558, 2), 131072, 8]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(444, 65558, F4, 7) (dual of [65558, 65514, 8]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(442, 65554, F4, 7) (dual of [65554, 65512, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(441, 65536, F4, 7) (dual of [65536, 65495, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(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(6) ⊂ Ce(4) [i] based on
- linear OA(442, 65556, F4, 6) (dual of [65556, 65514, 7]-code), using Gilbert–Varšamov bound and bm = 442 > Vbs−1(k−1) = 2 451313 900934 462172 681304 [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, using
- linear OA(442, 65554, F4, 7) (dual of [65554, 65512, 8]-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(444, 32779, F4, 3, 7) (dual of [(32779, 3), 98293, 8]-NRT-code) | [i] | OOA Folding | |