Information on Result #1315763
Linear OA(6437, 4212, F64, 16) (dual of [4212, 4175, 17]-code), using 108 step Varšamov–Edel lengthening with (ri) = (4, 4 times 0, 1, 20 times 0, 1, 81 times 0) based on linear OA(6431, 4098, F64, 16) (dual of [4098, 4067, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- linear OA(6431, 4096, F64, 16) (dual of [4096, 4065, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(6429, 4096, F64, 15) (dual of [4096, 4067, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 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
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(6437, 4212, F64, 2, 16) (dual of [(4212, 2), 8387, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6437, 4212, F64, 3, 16) (dual of [(4212, 3), 12599, 17]-NRT-code) | [i] | ||
| 3 | Digital (21, 37, 4212)-net over F64 | [i] | ||
| 4 | Linear OOA(6437, 2106, F64, 2, 16) (dual of [(2106, 2), 4175, 17]-NRT-code) | [i] | OOA Folding | |