Information on Result #1420327
Linear OOA(459, 4194332, F4, 2, 7) (dual of [(4194332, 2), 8388605, 8]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(459, 4194332, F4, 7) (dual of [4194332, 4194273, 8]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(457, 4194328, F4, 7) (dual of [4194328, 4194271, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(456, 4194304, F4, 7) (dual of [4194304, 4194248, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(423, 24, F4, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,4)), using
- dual of repetition code with length 24 [i]
- linear OA(41, 24, F4, 1) (dual of [24, 23, 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(457, 4194330, F4, 6) (dual of [4194330, 4194273, 7]-code), using Gilbert–Varšamov bound and bm = 457 > Vbs−1(k−1) = 2628 673401 280249 707499 251064 741876 [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(457, 4194328, F4, 7) (dual of [4194328, 4194271, 8]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(459, 2097166, F4, 3, 7) (dual of [(2097166, 3), 6291439, 8]-NRT-code) | [i] | OOA Folding | |