Information on Result #1052689
Linear OOA(2251, 1048589, F2, 4, 22) (dual of [(1048589, 4), 4194105, 23]-NRT-code), using OOA 4-folding based on linear OA(2251, 4194356, F2, 22) (dual of [4194356, 4194105, 23]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2249, 4194354, F2, 22) (dual of [4194354, 4194105, 23]-code), using
- 1 times truncation [i] based on linear OA(2250, 4194355, F2, 23) (dual of [4194355, 4194105, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2243, 4194304, F2, 23) (dual of [4194304, 4194061, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2199, 4194304, F2, 19) (dual of [4194304, 4194105, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(27, 51, F2, 3) (dual of [51, 44, 4]-code or 51-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(22) ⊂ Ce(18) [i] based on
- 1 times truncation [i] based on linear OA(2250, 4194355, F2, 23) (dual of [4194355, 4194105, 24]-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(2252, 1048589, F2, 4, 22) (dual of [(1048589, 4), 4194104, 23]-NRT-code) | [i] | OOA Duplication | |