Information on Result #812949
Linear OOA(3115, 2391500, F3, 2, 12) (dual of [(2391500, 2), 4782885, 13]-NRT-code), using OOA 2-folding based on linear OA(3115, 4783000, F3, 12) (dual of [4783000, 4782885, 13]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3114, 4782999, F3, 12) (dual of [4782999, 4782885, 13]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(3113, 4782969, F3, 13) (dual of [4782969, 4782856, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(385, 4782969, F3, 10) (dual of [4782969, 4782884, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(329, 30, F3, 29) (dual of [30, 1, 30]-code or 30-arc in PG(28,3)), using
- dual of repetition code with length 30 [i]
- linear OA(31, 30, F3, 1) (dual of [30, 29, 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(3117, 2391501, F3, 2, 12) (dual of [(2391501, 2), 4782885, 13]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(3116, 2391500, F3, 2, 12) (dual of [(2391500, 2), 4782884, 13]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3115, 2028814, F3, 3, 12) (dual of [(2028814, 3), 6086327, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3115, 2028814, F3, 4, 12) (dual of [(2028814, 4), 8115141, 13]-NRT-code) | [i] | ||
| 5 | Linear OOA(3115, 2028814, F3, 5, 12) (dual of [(2028814, 5), 10143955, 13]-NRT-code) | [i] | ||
| 6 | Digital (103, 115, 2028814)-net over F3 | [i] | ||