Information on Result #952392
Linear OOA(3111, 177152, F3, 3, 14) (dual of [(177152, 3), 531345, 15]-NRT-code), using OOA 3-folding based on linear OA(3111, 531456, F3, 14) (dual of [531456, 531345, 15]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3110, 531455, F3, 14) (dual of [531455, 531345, 15]-code), using
- construction X4 applied to C([0,13]) ⊂ C([1,12]) [i] based on
- linear OA(3109, 531440, F3, 14) (dual of [531440, 531331, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(396, 531440, F3, 12) (dual of [531440, 531344, 13]-code), using the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(314, 15, F3, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,3)), using
- dual of repetition code with length 15 [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 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 C([0,13]) ⊂ C([1,12]) [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(3112, 177152, F3, 3, 14) (dual of [(177152, 3), 531344, 15]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3111, 177152, F3, 4, 14) (dual of [(177152, 4), 708497, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3111, 177152, F3, 5, 14) (dual of [(177152, 5), 885649, 15]-NRT-code) | [i] | ||
| 4 | Digital (97, 111, 177152)-net over F3 | [i] | ||