Information on Result #1151648
Linear OOA(2232, 299596, F2, 7, 22) (dual of [(299596, 7), 2096940, 23]-NRT-code), using OOA 7-folding based on linear OA(2232, 2097172, F2, 22) (dual of [2097172, 2096940, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2232, 2097173, F2, 22) (dual of [2097173, 2096941, 23]-code), using
- 1 times truncation [i] based on linear OA(2233, 2097174, F2, 23) (dual of [2097174, 2096941, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- linear OA(2232, 2097152, F2, 23) (dual of [2097152, 2096920, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2211, 2097152, F2, 21) (dual of [2097152, 2096941, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(21, 22, F2, 1) (dual of [22, 21, 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(22) ⊂ Ce(20) [i] based on
- 1 times truncation [i] based on linear OA(2233, 2097174, F2, 23) (dual of [2097174, 2096941, 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(2234, 299596, F2, 7, 22) (dual of [(299596, 7), 2096938, 23]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2235, 299596, F2, 7, 22) (dual of [(299596, 7), 2096937, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(2232, 299596, F2, 8, 22) (dual of [(299596, 8), 2396536, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (210, 232, 299596)-net over F2 | [i] | ||