Information on Result #2485398
Linear OOA(364, 29531, F3, 2, 10) (dual of [(29531, 2), 58998, 11]-NRT-code), using 31 times duplication based on linear OOA(363, 29531, F3, 2, 10) (dual of [(29531, 2), 58999, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(363, 59062, F3, 10) (dual of [59062, 58999, 11]-code), using
- 1 times code embedding in larger space [i] based on linear OA(362, 59061, F3, 10) (dual of [59061, 58999, 11]-code), using
- construction X4 applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(361, 59049, F3, 10) (dual of [59049, 58988, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(351, 59049, F3, 8) (dual of [59049, 58998, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(311, 12, F3, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,3)), using
- dual of repetition code with length 12 [i]
- linear OA(31, 12, F3, 1) (dual of [12, 11, 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 code embedding in larger space [i] based on linear OA(362, 59061, F3, 10) (dual of [59061, 58999, 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(364, 28427, F3, 3, 10) (dual of [(28427, 3), 85217, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(364, 28427, F3, 4, 10) (dual of [(28427, 4), 113644, 11]-NRT-code) | [i] | ||
| 3 | Linear OOA(364, 28427, F3, 5, 10) (dual of [(28427, 5), 142071, 11]-NRT-code) | [i] | ||
| 4 | Digital (54, 64, 28427)-net over F3 | [i] | ||