Information on Result #952481
Linear OOA(3144, 1594334, F3, 3, 15) (dual of [(1594334, 3), 4782858, 16]-NRT-code), using OOA 3-folding based on linear OA(3144, 4783002, F3, 15) (dual of [4783002, 4782858, 16]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3142, 4783000, F3, 15) (dual of [4783000, 4782858, 16]-code), using
- construction X4 applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(3141, 4782970, F3, 15) (dual of [4782970, 4782829, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(3113, 4782970, F3, 13) (dual of [4782970, 4782857, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [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 C([0,7]) ⊂ C([0,6]) [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(3145, 1594334, F3, 3, 15) (dual of [(1594334, 3), 4782857, 16]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3144, 1594334, F3, 4, 15) (dual of [(1594334, 4), 6377192, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3144, 1594334, F3, 5, 15) (dual of [(1594334, 5), 7971526, 16]-NRT-code) | [i] | ||
| 4 | Digital (129, 144, 1594334)-net over F3 | [i] | ||