Information on Result #2784610
Linear OOA(2218, 4104, F2, 4, 30) (dual of [(4104, 4), 16198, 31]-NRT-code), using 1 step truncation based on linear OOA(2219, 4105, F2, 4, 31) (dual of [(4105, 4), 16201, 32]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2219, 16420, F2, 31) (dual of [16420, 16201, 32]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2218, 16419, F2, 31) (dual of [16419, 16201, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- 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(2183, 16384, F2, 27) (dual of [16384, 16201, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(30) ⊂ Ce(26) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2218, 16419, F2, 31) (dual of [16419, 16201, 32]-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(2218, 3805, F2, 5, 30) (dual of [(3805, 5), 18807, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2218, 3805, F2, 6, 30) (dual of [(3805, 6), 22612, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(2218, 3805, F2, 7, 30) (dual of [(3805, 7), 26417, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(2218, 3805, F2, 8, 30) (dual of [(3805, 8), 30222, 31]-NRT-code) | [i] | ||
| 5 | Digital (188, 218, 3805)-net over F2 | [i] | ||