Information on Result #1466426
Linear OOA(3250, 4194508, F3, 2, 22) (dual of [(4194508, 2), 8388766, 23]-NRT-code), using (u, u+v)-construction based on
- linear OOA(339, 207, F3, 2, 11) (dual of [(207, 2), 375, 12]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(339, 207, F3, 11) (dual of [207, 168, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(339, 256, F3, 11) (dual of [256, 217, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(336, 243, F3, 11) (dual of [243, 207, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(326, 243, F3, 8) (dual of [243, 217, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(339, 256, F3, 11) (dual of [256, 217, 12]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(339, 207, F3, 11) (dual of [207, 168, 12]-code), using
- linear OOA(3211, 4194301, F3, 2, 22) (dual of [(4194301, 2), 8388391, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3211, 8388602, F3, 22) (dual of [8388602, 8388391, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3211, large, F3, 22) (dual of [large, large−211, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(3211, large, F3, 22) (dual of [large, large−211, 23]-code), using
- OOA 2-folding [i] based on linear OA(3211, 8388602, F3, 22) (dual of [8388602, 8388391, 23]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(3250, 4194508, F3, 3, 22) (dual of [(4194508, 3), 12583274, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3250, 4194508, F3, 4, 22) (dual of [(4194508, 4), 16777782, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(3250, 4194508, F3, 5, 22) (dual of [(4194508, 5), 20972290, 23]-NRT-code) | [i] | ||
| 4 | Digital (228, 250, 4194508)-net over F3 | [i] | ||