Information on Result #674735
Linear OA(346, 177171, F3, 6) (dual of [177171, 177125, 7]-code), using construction X4 applied to Ce(6) ⊂ Ce(3) 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
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 OA(347, 177172, F3, 6) (dual of [177172, 177125, 7]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(346, 177171, F3, 2, 6) (dual of [(177171, 2), 354296, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(346, 177171, F3, 3, 6) (dual of [(177171, 3), 531467, 7]-NRT-code) | [i] | ||
| 4 | Linear OOA(346, 177171, F3, 4, 6) (dual of [(177171, 4), 708638, 7]-NRT-code) | [i] | ||
| 5 | Linear OOA(346, 177171, F3, 5, 6) (dual of [(177171, 5), 885809, 7]-NRT-code) | [i] | ||
| 6 | Linear OA(347, 177173, F3, 6) (dual of [177173, 177126, 7]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OOA(346, 59057, F3, 3, 6) (dual of [(59057, 3), 177125, 7]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(346, 59057, F3, 4, 6) (dual of [(59057, 4), 236182, 7]-NRT-code) | [i] | OA Folding and Stacking | |
| 9 | Linear OOA(346, 59057, F3, 5, 6) (dual of [(59057, 5), 295239, 7]-NRT-code) | [i] | ||