Information on Result #1466420
Linear OOA(3244, 4194397, F3, 2, 22) (dual of [(4194397, 2), 8388550, 23]-NRT-code), using (u, u+v)-construction based on
- linear OOA(333, 96, F3, 2, 11) (dual of [(96, 2), 159, 12]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(333, 96, F3, 11) (dual of [96, 63, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(333, 97, F3, 11) (dual of [97, 64, 12]-code), using
- 1 times code embedding in larger space [i] based on linear OA(332, 96, F3, 11) (dual of [96, 64, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
- linear OA(327, 81, F3, 11) (dual of [81, 54, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(317, 81, F3, 7) (dual of [81, 64, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(35, 15, F3, 3) (dual of [15, 10, 4]-code or 15-cap in PG(4,3)), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(332, 96, F3, 11) (dual of [96, 64, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(333, 97, F3, 11) (dual of [97, 64, 12]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(333, 96, F3, 11) (dual of [96, 63, 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(3244, 4194397, F3, 3, 22) (dual of [(4194397, 3), 12582947, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3244, 4194397, F3, 4, 22) (dual of [(4194397, 4), 16777344, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(3244, 4194397, F3, 5, 22) (dual of [(4194397, 5), 20971741, 23]-NRT-code) | [i] | ||
| 4 | Digital (222, 244, 4194397)-net over F3 | [i] | ||