Information on Result #1052249
Linear OOA(2135, 4105, F2, 4, 19) (dual of [(4105, 4), 16285, 20]-NRT-code), using OOA 4-folding based on linear OA(2135, 16420, F2, 19) (dual of [16420, 16285, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2134, 16419, F2, 19) (dual of [16419, 16285, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(2127, 16384, F2, 19) (dual of [16384, 16257, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(299, 16384, F2, 15) (dual of [16384, 16285, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(27, 35, F2, 3) (dual of [35, 28, 4]-code or 35-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to Ce(18) ⊂ Ce(14) [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(2134, 4104, F2, 4, 18) (dual of [(4104, 4), 16282, 19]-NRT-code) | [i] | Truncation for OOAs | |
| 2 | Linear OOA(2135, 3945, F2, 5, 19) (dual of [(3945, 5), 19590, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2135, 3945, F2, 6, 19) (dual of [(3945, 6), 23535, 20]-NRT-code) | [i] | ||
| 4 | Linear OOA(2135, 3945, F2, 7, 19) (dual of [(3945, 7), 27480, 20]-NRT-code) | [i] | ||
| 5 | Linear OOA(2135, 3945, F2, 8, 19) (dual of [(3945, 8), 31425, 20]-NRT-code) | [i] | ||
| 6 | Digital (116, 135, 3945)-net over F2 | [i] | ||