Information on Result #812928
Linear OOA(383, 29536, F3, 2, 12) (dual of [(29536, 2), 58989, 13]-NRT-code), using OOA 2-folding based on linear OA(383, 59072, F3, 12) (dual of [59072, 58989, 13]-code), using
- 1 times code embedding in larger space [i] based on linear OA(382, 59071, F3, 12) (dual of [59071, 58989, 13]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(381, 59049, F3, 13) (dual of [59049, 58968, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- 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(321, 22, F3, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,3)), using
- dual of repetition code with length 22 [i]
- linear OA(31, 22, F3, 1) (dual of [22, 21, 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(12) ⊂ Ce(9) [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(385, 29537, F3, 2, 12) (dual of [(29537, 2), 58989, 13]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(384, 29536, F3, 2, 12) (dual of [(29536, 2), 58988, 13]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(383, 29536, F3, 3, 12) (dual of [(29536, 3), 88525, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(383, 29536, F3, 4, 12) (dual of [(29536, 4), 118061, 13]-NRT-code) | [i] | ||
| 5 | Linear OOA(383, 29536, F3, 5, 12) (dual of [(29536, 5), 147597, 13]-NRT-code) | [i] | ||
| 6 | Digital (71, 83, 29536)-net over F3 | [i] | ||