Information on Result #2799287
Linear OOA(3237, 398584, F3, 4, 28) (dual of [(398584, 4), 1594099, 29]-NRT-code), using 31 times duplication based on linear OOA(3236, 398584, F3, 4, 28) (dual of [(398584, 4), 1594100, 29]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3236, 1594336, F3, 28) (dual of [1594336, 1594100, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 1594337, F3, 28) (dual of [1594337, 1594101, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(3235, 1594323, F3, 28) (dual of [1594323, 1594088, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3222, 1594323, F3, 26) (dual of [1594323, 1594101, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(31, 14, F3, 1) (dual of [14, 13, 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 X applied to Ce(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(3236, 1594337, F3, 28) (dual of [1594337, 1594101, 29]-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(3237, 321249, F3, 5, 28) (dual of [(321249, 5), 1606008, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (209, 237, 321249)-net over F3 | [i] | ||