Information on Result #2677591
Linear OOA(3223, 1594345, F3, 3, 23) (dual of [(1594345, 3), 4782812, 24]-NRT-code), using 31 times duplication based on linear OOA(3222, 1594345, F3, 3, 23) (dual of [(1594345, 3), 4782813, 24]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3222, 4783035, F3, 23) (dual of [4783035, 4782813, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3222, 4783036, F3, 23) (dual of [4783036, 4782814, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(3211, 4782969, F3, 23) (dual of [4782969, 4782758, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3155, 4782969, F3, 17) (dual of [4782969, 4782814, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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 Ce(22) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(3222, 4783036, F3, 23) (dual of [4783036, 4782814, 24]-code), using
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(3223, 1326605, F3, 4, 23) (dual of [(1326605, 4), 5306197, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3223, 1326605, F3, 5, 23) (dual of [(1326605, 5), 6632802, 24]-NRT-code) | [i] | ||
| 3 | Digital (200, 223, 1326605)-net over F3 | [i] | ||