Information on Result #812729
Linear OOA(379, 797168, F3, 2, 9) (dual of [(797168, 2), 1594257, 10]-NRT-code), using OOA 2-folding based on linear OA(379, 1594336, F3, 9) (dual of [1594336, 1594257, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(379, 1594337, F3, 9) (dual of [1594337, 1594258, 10]-code), using
- 1 times truncation [i] based on linear OA(380, 1594338, F3, 10) (dual of [1594338, 1594258, 11]-code), using
- construction X4 applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(379, 1594323, F3, 10) (dual of [1594323, 1594244, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(366, 1594323, F3, 8) (dual of [1594323, 1594257, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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 Ce(9) ⊂ Ce(7) [i] based on
- 1 times truncation [i] based on linear OA(380, 1594338, F3, 10) (dual of [1594338, 1594258, 11]-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(379, 797168, F3, 3, 9) (dual of [(797168, 3), 2391425, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(379, 797168, F3, 4, 9) (dual of [(797168, 4), 3188593, 10]-NRT-code) | [i] | ||
| 3 | Linear OOA(379, 797168, F3, 5, 9) (dual of [(797168, 5), 3985761, 10]-NRT-code) | [i] | ||
| 4 | Digital (70, 79, 797168)-net over F3 | [i] | ||