Information on Result #1305694
Linear OA(3245, 2225, F3, 51) (dual of [2225, 1980, 52]-code), using 25 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 0, 0, 0, 1, 6 times 0, 1, 10 times 0) based on linear OA(3239, 2194, F3, 51) (dual of [2194, 1955, 52]-code), using
- 1 times truncation [i] based on linear OA(3240, 2195, F3, 52) (dual of [2195, 1955, 53]-code), using
- construction X applied to Ce(51) ⊂ Ce(49) [i] based on
- linear OA(3239, 2187, F3, 52) (dual of [2187, 1948, 53]-code), using an extension Ce(51) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,51], and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(3232, 2187, F3, 50) (dual of [2187, 1955, 51]-code), using an extension Ce(49) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,49], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(31, 8, F3, 1) (dual of [8, 7, 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(51) ⊂ Ce(49) [i] based on
Mode: 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(3245, 2225, F3, 2, 51) (dual of [(2225, 2), 4205, 52]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3245, 2225, F3, 3, 51) (dual of [(2225, 3), 6430, 52]-NRT-code) | [i] | ||
| 3 | Linear OOA(3245, 2225, F3, 4, 51) (dual of [(2225, 4), 8655, 52]-NRT-code) | [i] | ||
| 4 | Linear OOA(3245, 2225, F3, 5, 51) (dual of [(2225, 5), 10880, 52]-NRT-code) | [i] | ||
| 5 | Digital (194, 245, 2225)-net over F3 | [i] | ||