Information on Result #952395
Linear OOA(3118, 531445, F3, 3, 14) (dual of [(531445, 3), 1594217, 15]-NRT-code), using OOA 3-folding based on linear OA(3118, 1594335, F3, 14) (dual of [1594335, 1594217, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3118, 1594336, F3, 14) (dual of [1594336, 1594218, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(3118, 1594323, F3, 14) (dual of [1594323, 1594205, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(3105, 1594323, F3, 13) (dual of [1594323, 1594218, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(30, 13, F3, 0) (dual of [13, 13, 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
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
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(3118, 531445, F3, 4, 14) (dual of [(531445, 4), 2125662, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3118, 531445, F3, 5, 14) (dual of [(531445, 5), 2657107, 15]-NRT-code) | [i] | ||
| 3 | Digital (104, 118, 531445)-net over F3 | [i] | ||