Information on Result #1640797
Linear OOA(347, 177173, F3, 5, 6) (dual of [(177173, 5), 885818, 7]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(347, 177173, F3, 6) (dual of [177173, 177126, 7]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(346, 177171, F3, 6) (dual of [177171, 177125, 7]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(3) [i] based on
- linear OA(345, 177147, F3, 7) (dual of [177147, 177102, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(323, 177147, F3, 4) (dual of [177147, 177124, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(323, 24, F3, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,3)), using
- dual of repetition code with length 24 [i]
- linear OA(31, 24, F3, 1) (dual of [24, 23, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(6) ⊂ Ce(3) [i] based on
- linear OA(346, 177172, F3, 5) (dual of [177172, 177126, 6]-code), using Gilbert–Varšamov bound and bm = 346 > Vbs−1(k−1) = 656 854956 953745 793883 [i]
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(346, 177171, F3, 6) (dual of [177171, 177125, 7]-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(347, 177173, F3, 6, 6) (dual of [(177173, 6), 1062991, 7]-NRT-code) | [i] | Appending kth Column | |