Information on Result #735120
Linear OA(6436, 262212, F64, 11) (dual of [262212, 262176, 12]-code), using (u, u+v)-construction based on
- linear OA(645, 65, F64, 5) (dual of [65, 60, 6]-code or 65-arc in PG(4,64)), using
- extended Reed–Solomon code RSe(60,64) [i]
- the expurgated narrow-sense BCH-code C(I) with length 65 | 642−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(6431, 262147, F64, 11) (dual of [262147, 262116, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(6431, 262144, F64, 11) (dual of [262144, 262113, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(6428, 262144, F64, 10) (dual of [262144, 262116, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
Mode: Constructive and 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, 262212, F64, 2, 11) (dual of [(262212, 2), 524388, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6436, 262212, F64, 3, 11) (dual of [(262212, 3), 786600, 12]-NRT-code) | [i] | ||
| 3 | Digital (25, 36, 262212)-net over F64 | [i] | ||
| 4 | Linear OOA(6436, 131106, F64, 2, 11) (dual of [(131106, 2), 262176, 12]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(6436, 87404, F64, 3, 11) (dual of [(87404, 3), 262176, 12]-NRT-code) | [i] | ||
| 6 | Linear OOA(6436, 52442, F64, 11, 11) (dual of [(52442, 11), 576826, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |