Information on Result #1564356
Linear OOA(6444, 4211, F64, 3, 19) (dual of [(4211, 3), 12589, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(6444, 4211, F64, 19) (dual of [4211, 4167, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(6444, 4256, F64, 19) (dual of [4256, 4212, 20]-code), using
- 151 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 0, 1, 11 times 0, 1, 34 times 0, 1, 99 times 0) [i] based on linear OA(6437, 4098, F64, 19) (dual of [4098, 4061, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(6437, 4096, F64, 19) (dual of [4096, 4059, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(6435, 4096, F64, 18) (dual of [4096, 4061, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- 151 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 0, 1, 11 times 0, 1, 34 times 0, 1, 99 times 0) [i] based on linear OA(6437, 4098, F64, 19) (dual of [4098, 4061, 20]-code), 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(6444, 1403, F64, 21, 19) (dual of [(1403, 21), 29419, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |