Information on Result #1534110
Linear OOA(448, 262166, F4, 3, 7) (dual of [(262166, 3), 786450, 8]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(448, 262166, F4, 7) (dual of [262166, 262118, 8]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(447, 262164, F4, 7) (dual of [262164, 262117, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(446, 262144, F4, 7) (dual of [262144, 262098, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(428, 262144, F4, 5) (dual of [262144, 262116, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(419, 20, F4, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,4)), using
- dual of repetition code with length 20 [i]
- linear OA(41, 20, F4, 1) (dual of [20, 19, 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(447, 262165, F4, 6) (dual of [262165, 262118, 7]-code), using Gilbert–Varšamov bound and bm = 447 > Vbs−1(k−1) = 2507 705291 430083 372086 261972 [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(447, 262164, F4, 7) (dual of [262164, 262117, 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(448, 262165, F4, 9, 7) (dual of [(262165, 9), 2359437, 8]-NRT-code) | [i] | OOA Stacking with Additional Row | |