Information on Result #2486057
Linear OOA(3138, 797184, F3, 2, 15) (dual of [(797184, 2), 1594230, 16]-NRT-code), using 31 times duplication based on linear OOA(3137, 797184, F3, 2, 15) (dual of [(797184, 2), 1594231, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3137, 1594368, F3, 15) (dual of [1594368, 1594231, 16]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(3131, 1594323, F3, 16) (dual of [1594323, 1594192, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(392, 1594323, F3, 11) (dual of [1594323, 1594231, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(36, 45, F3, 3) (dual of [45, 39, 4]-code or 45-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(15) ⊂ Ce(10) [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(3138, 675614, F3, 3, 15) (dual of [(675614, 3), 2026704, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3138, 675614, F3, 4, 15) (dual of [(675614, 4), 2702318, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(3138, 675614, F3, 5, 15) (dual of [(675614, 5), 3377932, 16]-NRT-code) | [i] | ||
| 4 | Digital (123, 138, 675614)-net over F3 | [i] | ||