Information on Result #2865730
Linear OOA(2197, 13111, F2, 5, 24) (dual of [(13111, 5), 65358, 25]-NRT-code), using 21 times duplication based on linear OOA(2196, 13111, F2, 5, 24) (dual of [(13111, 5), 65359, 25]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2196, 65555, F2, 24) (dual of [65555, 65359, 25]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2193, 65552, F2, 24) (dual of [65552, 65359, 25]-code), using
- 1 times truncation [i] based on linear OA(2194, 65553, F2, 25) (dual of [65553, 65359, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(2193, 65536, F2, 25) (dual of [65536, 65343, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(2177, 65536, F2, 23) (dual of [65536, 65359, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(21, 17, F2, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- 1 times truncation [i] based on linear OA(2194, 65553, F2, 25) (dual of [65553, 65359, 26]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2193, 65552, F2, 24) (dual of [65552, 65359, 25]-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(2197, 12252, F2, 6, 24) (dual of [(12252, 6), 73315, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2197, 12252, F2, 7, 24) (dual of [(12252, 7), 85567, 25]-NRT-code) | [i] | ||
| 3 | Linear OOA(2197, 12252, F2, 8, 24) (dual of [(12252, 8), 97819, 25]-NRT-code) | [i] | ||
| 4 | Digital (173, 197, 12252)-net over F2 | [i] | ||