Information on Result #2790320
Linear OOA(2248, 4105, F2, 4, 34) (dual of [(4105, 4), 16172, 35]-NRT-code), using 21 times duplication based on linear OOA(2247, 4105, F2, 4, 34) (dual of [(4105, 4), 16173, 35]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2247, 16420, F2, 34) (dual of [16420, 16173, 35]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2245, 16418, F2, 34) (dual of [16418, 16173, 35]-code), using
- 1 times truncation [i] based on linear OA(2246, 16419, F2, 35) (dual of [16419, 16173, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(30) [i] based on
- linear OA(2239, 16384, F2, 35) (dual of [16384, 16145, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2211, 16384, F2, 31) (dual of [16384, 16173, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(34) ⊂ Ce(30) [i] based on
- 1 times truncation [i] based on linear OA(2246, 16419, F2, 35) (dual of [16419, 16173, 36]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2245, 16418, F2, 34) (dual of [16418, 16173, 35]-code), using
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(2248, 3938, F2, 5, 34) (dual of [(3938, 5), 19442, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2248, 3938, F2, 6, 34) (dual of [(3938, 6), 23380, 35]-NRT-code) | [i] | ||
| 3 | Linear OOA(2248, 3938, F2, 7, 34) (dual of [(3938, 7), 27318, 35]-NRT-code) | [i] | ||
| 4 | Linear OOA(2248, 3938, F2, 8, 34) (dual of [(3938, 8), 31256, 35]-NRT-code) | [i] | ||
| 5 | Digital (214, 248, 3938)-net over F2 | [i] | ||