Information on Result #946109
Linear OOA(2113, 687, F2, 3, 21) (dual of [(687, 3), 1948, 22]-NRT-code), using OOA 3-folding based on linear OA(2113, 2061, F2, 21) (dual of [2061, 1948, 22]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2112, 2060, F2, 21) (dual of [2060, 1948, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- 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(2100, 2048, F2, 19) (dual of [2048, 1948, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(20) ⊂ Ce(18) [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(2116, 688, F2, 3, 21) (dual of [(688, 3), 1948, 22]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(2114, 687, F2, 3, 21) (dual of [(687, 3), 1947, 22]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2115, 687, F2, 3, 21) (dual of [(687, 3), 1946, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(2113, 612, F2, 4, 21) (dual of [(612, 4), 2335, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(2113, 612, F2, 5, 21) (dual of [(612, 5), 2947, 22]-NRT-code) | [i] | ||
| 6 | Linear OOA(2113, 612, F2, 6, 21) (dual of [(612, 6), 3559, 22]-NRT-code) | [i] | ||
| 7 | Linear OOA(2113, 612, F2, 7, 21) (dual of [(612, 7), 4171, 22]-NRT-code) | [i] | ||
| 8 | Linear OOA(2113, 612, F2, 8, 21) (dual of [(612, 8), 4783, 22]-NRT-code) | [i] | ||
| 9 | Digital (92, 113, 612)-net over F2 | [i] | ||