Information on Result #2228140
Linear OA(345, 177159, F3, 6) (dual of [177159, 177114, 7]-code), using 1 times truncation based on linear OA(346, 177160, F3, 7) (dual of [177160, 177114, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [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(334, 177147, F3, 5) (dual of [177147, 177113, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(312, 13, F3, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,3)), using
- dual of repetition code with length 13 [i]
- linear OA(31, 13, F3, 1) (dual of [13, 12, 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
Mode: Constructive and 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(345, 177159, F3, 2, 6) (dual of [(177159, 2), 354273, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(345, 177159, F3, 3, 6) (dual of [(177159, 3), 531432, 7]-NRT-code) | [i] | ||
| 3 | Linear OOA(345, 177159, F3, 4, 6) (dual of [(177159, 4), 708591, 7]-NRT-code) | [i] | ||
| 4 | Linear OOA(345, 177159, F3, 5, 6) (dual of [(177159, 5), 885750, 7]-NRT-code) | [i] | ||
| 5 | Linear OOA(345, 88579, F3, 2, 6) (dual of [(88579, 2), 177113, 7]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(345, 59053, F3, 3, 6) (dual of [(59053, 3), 177114, 7]-NRT-code) | [i] | ||
| 7 | Linear OOA(345, 59053, F3, 4, 6) (dual of [(59053, 4), 236167, 7]-NRT-code) | [i] | OA Folding and Stacking | |
| 8 | Linear OOA(345, 59053, F3, 5, 6) (dual of [(59053, 5), 295220, 7]-NRT-code) | [i] | ||