Information on Result #2485686
Linear OOA(393, 88587, F3, 2, 12) (dual of [(88587, 2), 177081, 13]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(391, 88586, F3, 2, 12) (dual of [(88586, 2), 177081, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(391, 177172, F3, 12) (dual of [177172, 177081, 13]-code), using
- 1 times code embedding in larger space [i] based on linear OA(390, 177171, F3, 12) (dual of [177171, 177081, 13]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(389, 177147, F3, 13) (dual of [177147, 177058, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(367, 177147, F3, 10) (dual of [177147, 177080, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(12) ⊂ Ce(9) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(390, 177171, F3, 12) (dual of [177171, 177081, 13]-code), 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(393, 88587, F3, 3, 12) (dual of [(88587, 3), 265668, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(393, 88587, F3, 4, 12) (dual of [(88587, 4), 354255, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(393, 88587, F3, 5, 12) (dual of [(88587, 5), 442842, 13]-NRT-code) | [i] | ||
| 4 | Digital (81, 93, 88587)-net over F3 | [i] | ||