Information on Result #1315902
Linear OA(6472, 4476, F64, 31) (dual of [4476, 4404, 32]-code), using 364 step Varšamov–Edel lengthening with (ri) = (5, 0, 0, 1, 6 times 0, 1, 17 times 0, 1, 40 times 0, 1, 93 times 0, 1, 200 times 0) based on linear OA(6462, 4102, F64, 31) (dual of [4102, 4040, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,14]) [i] based on
- linear OA(6461, 4097, F64, 31) (dual of [4097, 4036, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(6457, 4097, F64, 29) (dual of [4097, 4040, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 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(6472, 4476, F64, 2, 31) (dual of [(4476, 2), 8880, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6472, 4476, F64, 3, 31) (dual of [(4476, 3), 13356, 32]-NRT-code) | [i] | ||
| 3 | Digital (41, 72, 4476)-net over F64 | [i] | ||
| 4 | Linear OOA(6472, 2238, F64, 2, 31) (dual of [(2238, 2), 4404, 32]-NRT-code) | [i] | OOA Folding | |