Information on Result #946343
Linear OOA(2141, 1376, F2, 3, 23) (dual of [(1376, 3), 3987, 24]-NRT-code), using OOA 3-folding based on linear OA(2141, 4128, F2, 23) (dual of [4128, 3987, 24]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2139, 4126, F2, 23) (dual of [4126, 3987, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2133, 4096, F2, 23) (dual of [4096, 3963, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2109, 4096, F2, 19) (dual of [4096, 3987, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(22) ⊂ 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(2141, 1376, F2, 3, 22) (dual of [(1376, 3), 3987, 23]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2142, 1376, F2, 3, 23) (dual of [(1376, 3), 3986, 24]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2143, 1376, F2, 3, 23) (dual of [(1376, 3), 3985, 24]-NRT-code) | [i] | ||
| 4 | Linear OOA(2140, 1375, F2, 3, 22) (dual of [(1375, 3), 3985, 23]-NRT-code) | [i] | Truncation for OOAs | |
| 5 | Linear OOA(2141, 1191, F2, 4, 23) (dual of [(1191, 4), 4623, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(2141, 1191, F2, 5, 23) (dual of [(1191, 5), 5814, 24]-NRT-code) | [i] | ||
| 7 | Linear OOA(2141, 1191, F2, 6, 23) (dual of [(1191, 6), 7005, 24]-NRT-code) | [i] | ||
| 8 | Linear OOA(2141, 1191, F2, 7, 23) (dual of [(1191, 7), 8196, 24]-NRT-code) | [i] | ||
| 9 | Linear OOA(2141, 1191, F2, 8, 23) (dual of [(1191, 8), 9387, 24]-NRT-code) | [i] | ||
| 10 | Digital (118, 141, 1191)-net over F2 | [i] | ||