Information on Result #1305707
Linear OA(3250, 2396, F3, 51) (dual of [2396, 2146, 52]-code), using 183 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 0, 0, 1, 5 times 0, 1, 10 times 0, 1, 16 times 0, 1, 24 times 0, 1, 32 times 0, 1, 39 times 0, 1, 45 times 0) based on linear OA(3240, 2203, F3, 51) (dual of [2203, 1963, 52]-code), using
- construction X applied to C([0,25]) ⊂ C([0,24]) [i] based on
- linear OA(3239, 2188, F3, 51) (dual of [2188, 1949, 52]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,25], and minimum distance d ≥ |{−25,−24,…,25}|+1 = 52 (BCH-bound) [i]
- linear OA(3225, 2188, F3, 49) (dual of [2188, 1963, 50]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,24], and minimum distance d ≥ |{−24,−23,…,24}|+1 = 50 (BCH-bound) [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 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
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(3250, 2396, F3, 2, 51) (dual of [(2396, 2), 4542, 52]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3250, 2396, F3, 3, 51) (dual of [(2396, 3), 6938, 52]-NRT-code) | [i] | ||
| 3 | Linear OOA(3250, 2396, F3, 4, 51) (dual of [(2396, 4), 9334, 52]-NRT-code) | [i] | ||
| 4 | Linear OOA(3250, 2396, F3, 5, 51) (dual of [(2396, 5), 11730, 52]-NRT-code) | [i] | ||
| 5 | Digital (199, 250, 2396)-net over F3 | [i] | ||
| 6 | Linear OOA(3250, 1198, F3, 2, 51) (dual of [(1198, 2), 2146, 52]-NRT-code) | [i] | OOA Folding | |