Information on Result #2667456
Linear OOA(2126, 687, F2, 3, 23) (dual of [(687, 3), 1935, 24]-NRT-code), using 22 times duplication based on linear OOA(2124, 687, F2, 3, 23) (dual of [(687, 3), 1937, 24]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2124, 2061, F2, 23) (dual of [2061, 1937, 24]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2123, 2060, F2, 23) (dual of [2060, 1937, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- linear OA(2122, 2048, F2, 23) (dual of [2048, 1926, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2111, 2048, F2, 21) (dual of [2048, 1937, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 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 code embedding in larger space [i] based on linear OA(2123, 2060, F2, 23) (dual of [2060, 1937, 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(2126, 678, F2, 4, 23) (dual of [(678, 4), 2586, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2126, 678, F2, 5, 23) (dual of [(678, 5), 3264, 24]-NRT-code) | [i] | ||
| 3 | Linear OOA(2126, 678, F2, 6, 23) (dual of [(678, 6), 3942, 24]-NRT-code) | [i] | ||
| 4 | Linear OOA(2126, 678, F2, 7, 23) (dual of [(678, 7), 4620, 24]-NRT-code) | [i] | ||
| 5 | Linear OOA(2126, 678, F2, 8, 23) (dual of [(678, 8), 5298, 24]-NRT-code) | [i] | ||
| 6 | Digital (103, 126, 678)-net over F2 | [i] | ||