Information on Result #1052755
Linear OOA(2163, 4105, F2, 4, 23) (dual of [(4105, 4), 16257, 24]-NRT-code), using OOA 4-folding based on linear OA(2163, 16420, F2, 23) (dual of [16420, 16257, 24]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2162, 16419, F2, 23) (dual of [16419, 16257, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2155, 16384, F2, 23) (dual of [16384, 16229, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2127, 16384, F2, 19) (dual of [16384, 16257, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(27, 35, F2, 3) (dual of [35, 28, 4]-code or 35-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), 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(2164, 4105, F2, 4, 23) (dual of [(4105, 4), 16256, 24]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2165, 4105, F2, 4, 23) (dual of [(4105, 4), 16255, 24]-NRT-code) | [i] | ||
| 3 | Linear OOA(2162, 4104, F2, 4, 22) (dual of [(4104, 4), 16254, 23]-NRT-code) | [i] | Truncation for OOAs | |
| 4 | Linear OOA(2163, 3419, F2, 5, 23) (dual of [(3419, 5), 16932, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(2163, 3419, F2, 6, 23) (dual of [(3419, 6), 20351, 24]-NRT-code) | [i] | ||
| 6 | Linear OOA(2163, 3419, F2, 7, 23) (dual of [(3419, 7), 23770, 24]-NRT-code) | [i] | ||
| 7 | Linear OOA(2163, 3419, F2, 8, 23) (dual of [(3419, 8), 27189, 24]-NRT-code) | [i] | ||
| 8 | Digital (140, 163, 3419)-net over F2 | [i] | ||