Information on Result #806214
Linear OOA(291, 517, F2, 2, 18) (dual of [(517, 2), 943, 19]-NRT-code), using OOA 2-folding based on linear OA(291, 1034, F2, 18) (dual of [1034, 943, 19]-code), using
- 1 times truncation [i] based on linear OA(292, 1035, F2, 19) (dual of [1035, 943, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(291, 1024, F2, 19) (dual of [1024, 933, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(281, 1024, F2, 17) (dual of [1024, 943, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(21, 11, F2, 1) (dual of [11, 10, 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(18) ⊂ Ce(16) [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(291, 372, F2, 3, 18) (dual of [(372, 3), 1025, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(291, 372, F2, 4, 18) (dual of [(372, 4), 1397, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(291, 372, F2, 5, 18) (dual of [(372, 5), 1769, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(291, 372, F2, 6, 18) (dual of [(372, 6), 2141, 19]-NRT-code) | [i] | ||
| 5 | Linear OOA(291, 372, F2, 7, 18) (dual of [(372, 7), 2513, 19]-NRT-code) | [i] | ||
| 6 | Linear OOA(291, 372, F2, 8, 18) (dual of [(372, 8), 2885, 19]-NRT-code) | [i] | ||
| 7 | Digital (73, 91, 372)-net over F2 | [i] | ||