Information on Result #1305704
Linear OA(3247, 2274, F3, 51) (dual of [2274, 2027, 52]-code), using 64 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) 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(3247, 2274, F3, 2, 51) (dual of [(2274, 2), 4301, 52]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3247, 2274, F3, 3, 51) (dual of [(2274, 3), 6575, 52]-NRT-code) | [i] | ||
| 3 | Linear OOA(3247, 2274, F3, 4, 51) (dual of [(2274, 4), 8849, 52]-NRT-code) | [i] | ||
| 4 | Linear OOA(3247, 2274, F3, 5, 51) (dual of [(2274, 5), 11123, 52]-NRT-code) | [i] | ||
| 5 | Digital (196, 247, 2274)-net over F3 | [i] | ||
| 6 | Linear OOA(3247, 1137, F3, 2, 51) (dual of [(1137, 2), 2027, 52]-NRT-code) | [i] | OOA Folding | |