Information on Result #1315761
Linear OA(6436, 4682, F64, 15) (dual of [4682, 4646, 16]-code), using 574 step Varšamov–Edel lengthening with (ri) = (3, 6 times 0, 1, 28 times 0, 1, 118 times 0, 1, 418 times 0) based on linear OA(6430, 4102, F64, 15) (dual of [4102, 4072, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(6429, 4097, F64, 15) (dual of [4097, 4068, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(6425, 4097, F64, 13) (dual of [4097, 4072, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (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(6436, 4682, F64, 2, 15) (dual of [(4682, 2), 9328, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6436, 4682, F64, 3, 15) (dual of [(4682, 3), 14010, 16]-NRT-code) | [i] | ||
| 3 | Digital (21, 36, 4682)-net over F64 | [i] | ||
| 4 | Linear OOA(6436, 2341, F64, 2, 15) (dual of [(2341, 2), 4646, 16]-NRT-code) | [i] | OOA Folding | |