Information on Result #2484905
Linear OOA(356, 797170, F3, 2, 7) (dual of [(797170, 2), 1594284, 8]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(354, 797169, F3, 2, 7) (dual of [(797169, 2), 1594284, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(354, 1594338, F3, 7) (dual of [1594338, 1594284, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(353, 1594323, F3, 7) (dual of [1594323, 1594270, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(340, 1594323, F3, 5) (dual of [1594323, 1594283, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(6) ⊂ Ce(4) [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(356, 797170, F3, 3, 7) (dual of [(797170, 3), 2391454, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(356, 797170, F3, 4, 7) (dual of [(797170, 4), 3188624, 8]-NRT-code) | [i] | ||
| 3 | Linear OOA(356, 797170, F3, 5, 7) (dual of [(797170, 5), 3985794, 8]-NRT-code) | [i] | ||
| 4 | Digital (49, 56, 797170)-net over F3 | [i] | ||