Information on Result #1315903
Linear OA(6473, 4867, F64, 31) (dual of [4867, 4794, 32]-code), using 754 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, 1, 389 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(6473, 4867, F64, 2, 31) (dual of [(4867, 2), 9661, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6473, 4867, F64, 3, 31) (dual of [(4867, 3), 14528, 32]-NRT-code) | [i] | ||
| 3 | Digital (42, 73, 4867)-net over F64 | [i] | ||