Information on Result #2266730
Linear OA(3214, 6606, F3, 38) (dual of [6606, 6392, 39]-code), using 2 times code embedding in larger space based on linear OA(3212, 6604, F3, 38) (dual of [6604, 6392, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(31) [i] based on
- linear OA(3201, 6561, F3, 38) (dual of [6561, 6360, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3169, 6561, F3, 32) (dual of [6561, 6392, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(311, 43, F3, 5) (dual of [43, 32, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-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(3214, 4715, F3, 2, 38) (dual of [(4715, 2), 9216, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3214, 4715, F3, 3, 38) (dual of [(4715, 3), 13931, 39]-NRT-code) | [i] | ||
| 3 | Linear OOA(3214, 4715, F3, 4, 38) (dual of [(4715, 4), 18646, 39]-NRT-code) | [i] | ||
| 4 | Linear OOA(3214, 4715, F3, 5, 38) (dual of [(4715, 5), 23361, 39]-NRT-code) | [i] | ||
| 5 | Digital (176, 214, 4715)-net over F3 | [i] | ||
| 6 | Linear OOA(3214, 2202, F3, 3, 38) (dual of [(2202, 3), 6392, 39]-NRT-code) | [i] | OOA Folding | |