Information on Result #953068
Linear OOA(3209, 1594346, F3, 3, 21) (dual of [(1594346, 3), 4782829, 22]-NRT-code), using OOA 3-folding based on linear OA(3209, 4783038, F3, 21) (dual of [4783038, 4782829, 22]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3208, 4783037, F3, 21) (dual of [4783037, 4782829, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,7]) [i] based on
- linear OA(3197, 4782970, F3, 21) (dual of [4782970, 4782773, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- 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(311, 67, F3, 5) (dual of [67, 56, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to C([0,10]) ⊂ C([0,7]) [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(3209, 1594346, F3, 4, 21) (dual of [(1594346, 4), 6377175, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3209, 1594346, F3, 5, 21) (dual of [(1594346, 5), 7971521, 22]-NRT-code) | [i] | ||
| 3 | Digital (188, 209, 1594346)-net over F3 | [i] | ||