Information on Result #2677102
Linear OOA(3173, 1594334, F3, 3, 18) (dual of [(1594334, 3), 4782829, 19]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3170, 1594333, F3, 3, 18) (dual of [(1594333, 3), 4782829, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3170, 4782999, F3, 18) (dual of [4782999, 4782829, 19]-code), using
- construction X4 applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(3169, 4782969, F3, 19) (dual of [4782969, 4782800, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3141, 4782969, F3, 16) (dual of [4782969, 4782828, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(18) ⊂ Ce(15) [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(3173, 1594334, F3, 4, 18) (dual of [(1594334, 4), 6377163, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3173, 1594334, F3, 5, 18) (dual of [(1594334, 5), 7971497, 19]-NRT-code) | [i] | ||
| 3 | Digital (155, 173, 1594334)-net over F3 | [i] | ||